Symposium QN06—Emerging Materials for Quantum Information

Ettore Majorana famously considered that there may be fermions in nature that are their own antiparticle — and then he mysteriously disappeared just after proposing the idea in 1938. In recent years, following pioneering theoretical work of Kitaev and others, we have learned how to engineer materials that harbor quasiparticles that behave similar to fermions Majorana had envisioned. In particular, there has been a focus on one-dimensional topological superconductor that harbor Majorana zero modes (MZM) that can potentially be used to make fault-tolerant topological quantum computation possible. Recently, we have proposed and implemented a platform for realization of topological superconductivity and MZM in chains of magnetic atoms on the surface of a superconductor [1,2]. In this talk, I will describe this platform and the series of experiments we have performed to establish the presence of these exotic quasi-particle using spectroscopic mapping with the scanning tunneling microscope (STM). [2-4] These include study of the unique spin signature of MZM.[4] Finally, if there is time I will discuss our most recent work on realization of MZM in a platform based on chiral quantum spin Hall edge states [5]. Overall these experiments, illustrate how the power of spectroscopic imaging with the STM can be used to visualize novel quantum states of matter and their exotic quasi-particles.
[1] S. Nadj-Perge et al. PRB 88, 020407 (2013).
[2] S. Nadj-Perge et al. Science 346, 6209 (2014).
[3] B. E. Feldman et al. Nature Physics 13, 286 (2016).
[4] S. Jeon et al. Science 358, 772 (2017)
[5] B. Jack et al. in preparation (2018).

I will review recent theoretical developments in the field of topological quantum computing, in particular, I will focus on schemes based on Majorana fermions. For Majorana physics, a central ingredient is the proximity effect induced by a superconductor in some attached material. In particular, semiconducting quantum wires defined within 2DEGs and strongly coupled to thin superconducting epitaxial layers have been extensively explored in many experiments as promising platforms to host Majorana bound states. I will present our numerical and analytical studies of such geometries with proximity effects [1-5] where the strong coupling can lead to unwanted ‘metallization’ of the semiconductor host. I will also show that Andreev bound states in absence of any topological phase can mimick the zero-energy behavior of Majorana bound states as function of magnetic field [6].

References
[1] J. Klinovaja and D. Loss, Phys. Rev. B 90, 045118 (2014)
[2] C. Reeg, J. Klinovaja, and D. Loss, Phys. Rev. B 96, 081301 (2017)
[3] C. Reeg, D. Loss, and J. Klinovaja, Phys. Rev. B 97, 165425 (2018)
[4] C. Reeg, J. Klinovaja, and D. Loss, Beilstein Journal of Nanotechnology 9, 1263 (2018)
[5] C. Reeg, O. Dmytruk, D. Chevallier, D. Loss, and J. Klinovaja, arXiv:1810.09840

Majorana states in atomic-scale magnet-superconductor hybrid systems have recently become of great interest because they can encode topological qubits and ultimately provide a new direction in topological quantum computation [1,2].
First, it will be demonstrated how well defined 1D atomic chains of magnetic adatoms on superconducting substrates with high spin-orbit coupling can be artificially fabricated using STM-based atom-manipulation techniques. Spin-polarized STM measurements [3] allow to reveal the presence of non-collinear spin textures, i.e. spin spiral ground states, stabilized by interfacial Dzyaloshinskii-Moriya interactions [4,5]. Simultaneously performed scanning tunneling spectroscopy on the magnetic atom chains on the superconductor substrate reveal the evolution of the spatially and energetically resolved local density of states as well as the emergence of zero-energy bound states at the chain ends above a critical chain length. Based on the exact knowledge of the geometrical, electronic, and spin structure of the magnetic chain – superconductor hybrid system, the experimental results can be compared rigorously with ab-initio and model-type tight-binding calculations supporting the interpretation of the spectroscopic signatures at the ends of the chains as Majorana bound states [6]. More recently, the atomic-scale design of more complex network structures for Majorana state manipulation, including braiding operations has been in the focus of our research.
Second, we will address experimental and theoretical studies of monolayer topological superconductivity and chiral Majorana edge modes in model-type 2D magnetic islands on elemental superconductors [7]. In particular, we demonstrate that interface engineering by an atomically thin oxide layer is crucial for driving the studied hybrid system into a topologically non-trivial state as confirmed by theoretical calculations of the topological invariant, the Chern number.
Finally, the prospects for studies of Majorana states in skyrmion – superconductor hybrid systems [8] will be highlighted.

[1] J. Alicea et al., Nature Phys. 7, 412 (2011).
[2] S. Nadj-Perge et al., PRB 88, 20407 (2013); H.-Y. Hui et al., Sci. Rep.. 5, 8880 (2015).
[3] R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009).
[4] A. A. Khajetoorians et al., Nature Commun. 7, 10620 (2016).
[5] M. Steinbrecher et al., Nature Commun. 9, 2853 (2018).
[6] H. Kim et al., Science Advances 4, eaar5251 (2018).
[7] A. Palacio-Morales et al. (2018), arXiv:1809.04503.
[8] N. Romming et al., Science 341, 6146 (2013).

Incorporating superconductivity in topological states of matter offers potential routes to novel excitations with properties essential to topological quantum computation. Topological crystalline insulators (TCIs) are topological states of matter protected by crystalline symmetry rather than the more commonly used time-reversal invariant topological insulators. In this talk, we report on the fabrication of Josephson junctions using nanowires of SnTe, a TCI, as the weak link material. We show the divergence of our devices from standard Josephson junction behavior using DC techniques, highlighting intriguing novel behavior in the magnetic diffraction pattern, reminiscent of patterns observed in high temperature superconductors. This effect is explained in terms of a topological phase transition that happens in the junction at low temperatures.

Recent advances in coupling superconductivity to near surface InAs quantum wells (QWs) have allowed the observation of zero bias peaks suggestive of Majorana Zero Modes on a scalable platform[1]. This paves the way for lithographically defined complex nanostructured networks necessary for topological quantum computation. A semiconductor with high spin-orbit coupling should lead to a large induced topological gap and hence improved topological protection. Our efforts have focused on developing high mobility of near surface quantum wells of the high spin-orbit semiconductors InAs [2] and InSb. We have also investigated the growth of InAsySb1-y, which is expected to have higher spin-orbit coupling than either InAs or InSb. Epitaxial Al films are grown in-situ at low temperature so as to minimize interfacial reactions and Al agglomeration on the surface[3]. We have found that due to the high surface mobility of Al even at room temperature, the Al surface must be passivated immediately after growth to prevent agglomeration. Rather than relying on post growth lithography and top down etching to form semiconductor nanowire structures, we have investigated epitaxial Al growth on atomic hydrogen cleaned MOVPE-grown vapor-liquid-solid InSb nanostructures[4] and in-vacuum chemical beam epitaxy selective area grown InAs nanowires[5]. Large zero bias peaks have been observed for these epitaxial Al/InSb nanowire structures[6]. In this presentation issues as well as progress in developing superconductor/III-V semiconductor heterostructures for topological quantum computer application will be discussed.

1 H. J. Suominen, et al., Phys. Rev. Letts. 119, 176805 (2017)
2 J. S. Lee, et al., ArXiv:, 1809.06971
3 J. Shabani,et al., Phys Rev B 93, 155402 (2016)
4 S. Gazibegovic,et al. Nature 548, 434 (2017)
5 J. S. Lee,et al., arXiv:, 1808.04563
6 H. Zhang, et al, Nature 556, 74 (2018)
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‘InSb nanowires are used to detect first signatures of quasi particles called Majorana fermions. Recently, different schemes for performing operations and uncovering the non-Abelian statistics of Majorana fermions are proposed. Such operations are fundamental for topological quantum computing. For such a universal computational architecture the realization of a near-perfect nanowire network assembly is needed in which Majorana states are coherently coupled.
Here, we demonstrate a generic process by which we can design any proposed braiding device by manipulating an InP substrate and thereby the nanowire growth position and orientation. This approach combines recent advances in materials growth and theoretical proposals. Our method leads to highly controlled growth of InSb nanowire networks with single crystalline wire-wire junctions. Additionally, nanowire “hashtag” structures are grown with a high yield and contacted. In these devices, the Aharonov–Bohm (AB) effect is observed, demonstrating phase coherent transport. These measurements reveal the high quality of these structures. This generic platform will open new applications in quantum information processing. Furthermore, these structures are well suited for epitaxial shadow growth of a superconductor on the nanowire facets. We study the growth of superconductors on nanowires and reveal the electronic properties. We finally discuss methods to fabricate a complete device in vacuum further advancing device performance.’

Nanotechnology allows modifying the structure of nanoobjects down to the atomic scale. Low dimensional quantum heterostructures can be created in a nanowire system in order to modify its properties at will, e.g.: hybrid semiconductor-superconductor nanowire based quantum networks.
The aim of these new hybrid systems is to take advantage of Majorana pairs as the building blocks for the generation of qubits, which are the fundamental units of information in quantum computation. The configuration that would suit this application the most is the interface between a semiconductor and a superconductor, and an appropriate way to build them is to arrange them in a nanowire, which creates the so-called concept of proximitized nanowires. The selected semiconductors are usually InAs or InSb, while Al is mainly used as the superconductor, due to its theoretical transition to topological phase under certain chemical potential and external applied magnetic field conditions. In fact, reaching the material’s topological phase is a fundamental requirement to achieve the Majorana Zero Modes (MZMs), and for them to materialize it is mandatory to create thoroughly ordered and epitaxial heterojunctions, as well as perfectly grown materials (as well as specific requirements for each of the materials implied), that avoid the disorder-based scattering that can prevent the transition or even the failure of the topological regime. Incredible efforts are being made to avoid the so unwanted decoherence of the electrons and to directly apply the signatures of MZMs (basically conductance peaks) into real devices for quantum computing, as up to date, the total number and stability of the created qubits is not enough for a functional quantum processor. These qubits are based on binary gates that control the interaction between the Majorana pairs, and it is actually this interaction what can produce the quantum phenomenon based on the superposition of states. Indeed, in order to achieve in the future a direct observation of the theoretical properties of the MZMs, defect free, relaxed and perfectly epitaxial heterostructures are needed. In order to fulfill the above approach, several growth methodologies have been used: (1) vapour–liquid–solid (VLS) vertical nanowire growth and the posterior nanowire nanopositioning and contacting into the selected circuits, (2) VLS nanowire networks grown by using trenches on etched substrates, (3) guided-growth nanowires or (4) the newly developed selected area grown nanowire networks directly epitaxed on top of the substrates.
These newly developed hybrid quantum devices benefit from the new advances in growth methodologies, as mentioned above. However, in order to obtain the most outstanding conditions to achieve the MZMs we will need to assure perfect growth conditions. In the present work, we will present how an accurate knowledge on the atomic positions, down to single atom detection, may help to deeply understand the improved properties of our complex nanowire heterostructures. We will show how from scanning transmission electron microscopy (STEM) and related spectroscopies, it is possible to obtain precise 3D atomic models of our hybrid systems and understand the growth mechanisms in detail. Atomic scale strain studies will allow to observe the different relaxation mechanisms based on plastic and elastic deformations and visualize the defects induced to the nanowire structures that might be detrimental of their quantum properties. Special attention will be put on the superconductor-semiconductor heterointerface.

[1] M. Friedl, et al., Nano Letters, 18, 2666 (2018)
[2] S. Vaitiekenas, et al., Physical Review Letters, 121, 147701 (2018)
[3] F. Krizek, et al., Physical Review Materials, 2, 093401 (2018)

With its large g-factor, strong spin-orbit coupling and low effective mass, InSb is a candidate to host Majorana Zero Modes (MZMs) when coupled to a s-wave superconductor. While InSb nanowires epitaxially coupled to Al have already experimentally demonstrate their ability to generate MZMs [1], the realization of planar superconductor-semiconductor hybrid heterostructures is required to improve scalability and fabricate more and more complex networks with top-down lithography and gating.
We will first report on the growth developments of InSb two-dimensional electron gas (2DEGs) on GaAs (100) substrates. These structures exhibit high carrier mobility up to 190,000 cm²/Vs and have provided the first observation of induced superconductivity in InSb 2DEGs using Josephson junctions made with ex-situ deposited NbTiN electrodes. The in-situ epitaxial deposition of Al on top of these InSb 2DEGs will also be reported. Careful optimization of the Al deposition conditions and of the heterostructure design at the vicinity of the Al-InSb interface have been required to prevent Al-Sb intermixing [2] and to measure the first evidences of coupling between Al and InSb 2DEGs. These results are an important step toward generating MZMs with InSb 2DEGs.


[1] H. Zhang et al., Nature, 556, 74–79, (2018).
[2] F. Boscherini et al., Physical Review B, 35, 9580-9585, (1987).

MBE grown material based upon hybrid semiconductor-superconductor has generated a lot of interest recently due to the possibility that it allows for the emergence of Majorana Zero Modes (MZM) which may offer topological protection for quantum computing. [1]

Relevant material platforms for MZM based devices include semiconductors with high spin-orbit coupling such as InAs on GaSb, and InAs on InP which are coupled to a s-wave superconductor that shows 2e periodicity in a closed system. Thin aluminum films, ~7nm, meet these requirements and have been shown to have a high critical in-plane magnetic field. Additionally, the aluminum has remarkable epitaxial relationship with InAs allowing for atomic ordering of Al (111) and Al (110) parallel to InAs (100). [2]

Here we will show how the growth of thin epitaxial aluminum is extremely sensitive to temperature. Deposition or working at T>0°C causes many grains to form or the film to ball up while deposition of Al films at T~77°K shows good morphology but not the requisite crystallinity. Thin films, <10nm, deposited within the good temperature window on planar material, show structure which matches the semiconductor and has two distinct in-plane orientations, both are (111) in plane. This Al-InAs hybrid system shows an induced gap >200µeV. We present structural characterization of superconducting Al layers on MZM structures.

[1] S. Das Sarma, et. all, npj Quantum Information (2015). doi:10.1038/npjqi.2015.1
[2] P. Krogstrup et. all, Nature Materials (2015). doi:10.1038/nmat4176

Author for correspondence: [email protected]

Epitaxial Al-InAs structures are prime candidates for tunable superconducting qubits, the so-called “gatemon” where the Josephson energy can be tuned in-situ with an applied electric field to an InAs Josephson junction, eliminating the need for flux tuning in superconducting qubits [1]. Here we have characterized microwave cavities needed for coupling to superconducting gatemon qubits. We present resonator quality factors for a fixed design on various levels of the buffer layers used as substrates. We make a comparison to bare InP and Si to establish a comparative baseline. We study the relationship of anharmonicity in gatemon qubits to interface transparency in the Superconductor-Semiconductor structure.
[1] Larsen et al., Phys. Rev. Lett. 115, 127001 (2015).
We acknowledge support from the US Army Office of Research, ARO: W911NF-18-1-0067

Material development holds promise as the basis of topological quantum computing with Majorana fermions. These quasiparticles have been predicted at ends of semiconductor nanowires coupled to conventional superconductors [1-2]. These predictions were followed by a series of experiments providing transport signatures consistent with these theories [3-4]. These early measurements suffered from soft induced superconducting gap, which later was significantly improved by growing epitaxial semiconductor-superconductor (SE-SU) nanowires [5-6]. In order to reach the topological phase, an external magnetic field is needed to lift the spin degeneracy in these SE-SU systems, which brings an even larger challenge for achieving scalable solutions. Therefore, in order to integrate and scale up a topological quantum plane, materials that are intrinsically topological (without the need for an external applied field) would be highly preferable. Composite tri-crystals using ferromagnetic insulators (FMIs) in close proximity to the SE-SU structure have been proposed as a solution to lift the spin degeneracy [7], where the Zeeman splitting could be induced by the exchange field from the FMI.

In this work, we study hybrid SE-FMI epitaxy of EuS on different InAs crystallographic platforms as the initial basis of tri-crystal SE-SU-FMI NW systems. These SE-FMI systems prove to fullfil key requirements for the realization of topological quantum computing material without need of large external magnetic field:
1. The EuS thin film grown on (100) Zinc Blende InAs surface is fully conherent.
2. An exchange field exists by inducing magnetic moments into InAs of about 2 nm.
3. InAs/EuS NWs have strong shape-defined single magnetic domains along the NW length with Curie temperature of 19 K.
The results not only show the InAs/EuS hybrid crystals as promising candidates for topological quantum computing, but also confirm EuS as a promising FMI for various spin applications.

[1] R. M. Lutchyn, J. D. Sau, S. Das Sarma, Phys. Rev. Lett., 2010, 105, 077001.
[2] Y. Oreg, G. Refael, F. von Oppen, Phys. Rev. Lett., 2010, 105, 177002.
[3] V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, L. P. Kouwenhoven, Science, 2012, 336, 1003-1007.
[4] A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, H. Shtrikman, Nat. Phys., 2012, 8, 887-895.
[5] P. Krogstrup, N. L. B. Ziino, W. Chang, S. M. Albrecht, M. H. Madsen, E. Johnson, J. Nygard, C. M. Marcus, T. S. Jespersen, Nat. Mater., 2015, 14, 400-406.
[6] W. Chang, S. M. Albrecht, T. S. Jespersen, F. Kuemmeth, P. Krogstrup, J. Nygard, C. M. Marcus, Nat. Nanotechnol., 2015, 10, 232-236.
[7] J. D. Sau, R. M. Lutchyn, S. Tewari, S. Das Sarma, Phys. Rev. Lett., 2010, 104, 040502.

Ion traps are promising candidates for the physical implementation of quantum computing, but they suffer from excessive heating that limits the fidelity of quantum logic gates in practice. This "anomalous heating" is much greater than expected Johnson-Nyquist noise levels and manifests itself in ion motional heating that leads to decoherence. Previous studies have pinpointed dipole fluctuations of molecules adsorbed on the surfaces of ion trap electrodes as a likely source of anomalous heating but disagree on the mechanisms behind such heating, with a range of different dependencies on temperature, trap frequency, and ion-electrode distance predicted. Experimental spectra have shown a frequency dependence of roughly 1/ω on heating in the MHz regime. Meanwhile, previous simulations on individual adsorbates run by our group using kinetic Monte Carlo yielded multiple frequency regimes, with adsorbate-dependent levels of white noise at lower frequencies transitioning to 1/ω² scaling at higher frequencies. To bridge these findings, molecular dynamics (MD) simulations at long timescales were carried out on monolayer and sub monolayer adsorbate coverages on an Au (111) FCC electrode surface across a range of temperatures. These simulations feature many adsorbates at once traversing a jagged interpolated DFT-generated potential energy surface, enabling the model to more realistically explore the effects of adsorbate coverage and intermolecular interactions. The frequency spectra obtained from these high density, long timescale runs recovers a portion of the 1/ω scaling, in between the previously observed white noise and 1/ω² scaling, alluding to the impact that adsorbate coverages have on the overall frequency scaling of electrode heating rates.

Aluminum oxide (AlO_x) is extensively utilized as the tunnel barrier or the gate dielectric in quantum information (QI) devices. However, AlO_x often has a wide distribution of defects originating from the nonequilibrium structure, which affects the electrical stability of devices containing AlO_x. One manifestation of the device instability that is often observed on single-electron transistors (SETs) is a time instability named charge offset drift, which is a nanoscale probe of sub-1 e charged defect motion. In this work, we present excellent long-term charge offset stability (very small charge offset drift) measured from two types of SETs containing AlO_x: all- metallic AlO_x tunnel junction-based devices and tunable barrier silicon metal-oxide-semiconductor (MOS) devices. For the all-metallic devices, plasma-oxidized AlO_x is used as the tunnel barrier and the device fine structure is fabricated by double-angle e-beam evaporation. The long-term charge offset stability measured from these devices are better than any other reported metallic SETs, with very small linear charge offset drift of < 0.1 e and standard deviation of < 0.01 e over 7.5 days. For the silicon MOS devices, thermally-oxidized AlO_x is used to electrically isolate overlapping layers of aluminum gates and the devices are made on a silicon-on-insulator (SOI) substrate. These devices display a linear drift of < 0.07 e and standard deviation of < 0.02 e over 7 days. The above results demonstrate good electrical stability using AlO_x, which opens the future for large-scale device integration and improving qubit performance.

Many novel materials are being actively considered for quantum information science and for realizing high performance qubit operation at room temperature. It is known that deep defects in wide-band gap semiconductors can have spin states and long coherence times suitable for qubit operation. We theoretically investigate from ab-initio density functional theory (DFT) that the defect states in the hexagonal silicon carbide (4H-SiC) and boron nitride are potential qubit materials. The DFT supercell calculations were performed with the local-orbital and pseudopotential methods utilizing hybrid exchange-correlation functionals. Di-vacancies in SiC supercells yielded defect levels in the gap consisting of closely spaced doublet just above the valence band edge, and higher levels in the band gap. The divacancy with a spin state of 1 is charge neutral. The divacancy is characterized by C-dangling bonds and a Si-dangling bond. Jahn-teller distortions and formation energies as a function of the Fermi level will be discussed. Single photon interactions with these defect levels will be discussed. In contrast, the anti-site defects where C, Si are interchanged have high formation energies of 5.4 eV and have just a single shallow defect level close to the valence band edge, with no spin. We will compare results including the defect levels from both the electronic structure approaches. Simulations for BN will be compared with those of SiC. We will also discuss protypical (s,p) electron systems within group IIIA-IVA-VA elements and possible rare earth doped semiconductors for qubit operation.

Chemically prepared colloidal semiconductor quantum dots, most notably based on CdSe, have long been proposed as scalable and color-tunable single emitters for optical quantum information technologies. They have, however, suffered from prohibitively incoherent and unstable emission characterized by pronounced spectral diffusion and fluorescence intermittency at low temperatures.[1]
We now demonstrate that novel colloidal lead halide perovskite quantum dots (PQDs)[2,3] display a real utility as practical quantum emitters with unity emission efficiency and color-tunability over the entire visible spectral range. We show that a unique combination of long optical coherence times (T2 ~ 80 ps) and high oscillator strength (radiative lifetime T1 ~ 210 ps) at low temperatures, renders the emission of PQDs highly coherent.[4] Indeed, the degree of coherence (T2/2T1) already approaches values of self-assembled III-V quantum dots – even without cavity integration. Using photon-correlation-Fourier spectroscopy we furthermore demonstrate that the spectral stability of PQDs is drastically improved compared to established quantum dots and is already comparable to some nitrogen-vacancy centers in diamond. We attribute this superior spectral stability to the absence of surface-trap states in lead halide perovskite semiconductors. Together with the observed high single photon emission purity (g⁽²⁾(0) < 0.04) and high fraction of coherently emitted photons (~ 0.8), our results suggest that PQDs – unlike any other chemically-made semiconductor quantum dot material – can be explored as sources of indistinguishable single photons and entangled photon pairs for quantum information technologies. We present our ongoing synthetic efforts to further increase the optical coherence and reduce the inhomogeneous broadening, which is already as small as for typical self-assembled III-V quantum dots.
Our results suggest that lead halide perovskites – with their high defect tolerance and bright lowest-lying exciton state [5] – are promising semiconductors for the scalable production of quantum emitters with highly coherent emission that can be processed onto virtually any substrate and that benefit from the integration with hybrid nano-photonic components that has been demonstrated for colloidal materials. Unlike defect centers in diamond, PQDs can be rationally optimized via the structure of the quantum dot, a research effort that will require input from the quantum photonics and colloidal chemistry community.

[1] Aharonovich et al. Nature Photonics 10, pp. 631–641 (2016).
[2] Protesescu et al. Nano Lett., 15 , pp. 3692–3696 (2015).
[3] Krieg et al. ACS Energy Lett., 3 (3), pp. 641–646 (2018).
[4] Utzat et al. arXiv:1812.11923 (2018).
[5] Becker et al. Nature, 553, pp.189–193 (2018).

Quantum simulation represents a major research thrust in the growing field of quantum information. The visionary approach outlined by Feynman in 1982 aims to harness the ability of quantum systems to simulate their own behavior, while the Lloyd approach, aims to achieve “universal quantum simulation” by decomposing an arbitrary Hamiltonian into a sequence of quantum logic gates. The Feynman approach has been pursued with great success in the AMO community, and with increasing sophistication in the superconducting quantum community. We are developing a solid-state platform for quantum simulation based on a method for nanoscale control of the metal-insulator transition at the LaAlO₃/SrTiO₃ interface. This approach enables artificial electronic lattices to be constructed in up to two dimensions, and the strength and sign of electron-electron interactions (Hubbard U) can be programmed, enabling a wide range of quantum phases to be accessible (e.g., Mott insulator, superconductor). Because the LaAlO₃/SrTiO₃ medium is a real electronic system, synthesized quantum materials can interface with conventional electronic systems using well-established protocols. For example, a synthesized superconducting phase would really superconduct. Initial work has focused on one-dimensional Hamiltonians whose behavior can be analyzed using theoretical techniques such as density-matrix renormalization group (DMRG). We are currently transitioning to two-dimensional systems where the theoretical tools are much more limited. Solid-state quantum simulation offers new ways of speeding up quantum calculations that are currently intractable using state-of-the-art computational approaches running on classical hardware.

To fulfill the long-term vision of reliable quantum computation, the ideal hybrid platform allows quantum information to be processed, stored and transmitted on the same materials system [1]. Silicon can be a promising candidate for fault-tolerant hybrid quantum systems due to its multifunctionality and reliability as well as long coherence times [2]. Superconducting Si could provide a viable pathway for the realization of Si qubit circuits, by forming homogeneous Superconductor (SC)–Semiconductor–SC Josephson junctions. In this work, non-equilibrium p-doping of Si thin-films by homoepitaxial growth of Ga-rich Si on Si(111) is studied. MBE approach provides a closer control over Ga incorporation levels and thickness of Ga-rich interfacial layers. Surface structure and morphology of the p-doped films were evaluated in-situ by reflection high-energy electron diffraction (RHEED) and ex-situ by ambient atomic force microscopy (AFM). The doping levels and carrier concentrations were determined by temperature-dependent resistivity (ρ–T) measurements in 4-point van der Pauw and on Hall bars. Upon increase in Ga incorporation, ρ–T characteristics of the p-doped films transitioned from insulating to quasi-reentrant superconductivity with R_min/R_N of 0.82–0.89. Based on the known theories, primary growth mechanisms and strategies to go beyond the quasi-reentrant regime will be discussed.

This work is supported by the US Air Force Office of Scientific Research Young Investigator Award, FA9550-16-1-0348.

[1] Kurizki et al., PNAS 112, no. 13, 3866–3873 (2015).
[2] Shim et al., Nat. Comm. 5:4225 (2015).

Erbium, with optical transition in the 1.5um band is one of the attractive REI candidates for optical quantum memory. Recent studies have, overcome unique challenges that erbium presents and have shown coherence times exceeding 1 second in ¹⁶⁷Er. The coherence properties of REI are critically dependent on the host crystals, and methods of incorporating REI into the host structures play an important role as structural defects and impurities determine the local environment of the ions, which is an important factor contributing to linebroadening mechanisms.

Rare-earth oxides with low or no nuclear spin, such as CeO2 and Y2O3 are preferred host material for REI. The ability to tailor the properties of these systems on demand will be a powerful tool for quantum information applications. Molecular beam epitaxy (MBE) allows us to grow single crystal thin epitaxial films of certain RE oxides, and also enables precise control over the doping concentrations.

In this study Er-doped Y2O3 thin films were grown epitaxially on Si(111) using molecular beam epitaxy (MBE). Electron paramagnetic resonance (EPR) spectra of these samples show angular dependence of Er signal indicating crystalline quality of the host material. The site occupancy and crystalline environment of Er defect centers were studied by monitoring interplay between carrier concentration, film thickness and angular dependence of Er signal. The samples were grown using an oxygen plasma source and the EPR linewidth indicates an inverse dependence on the oxygen pressure during growth. PLE measurements show that Er atoms are present in the C2 and C3 sites substituting for Y. Further, preliminary results for optical linewidth parallel the dependence seen in EPR linewidth. In addition, post-growth anneal in an oxygen atmosphere shows improvement in the EPR and PLE signal intensity and the linewidth.

Temporal quantum coherence and control is foundational to the science and engineering of quantum systems. Improving such coherent characteristics in quantum systems, a key to realizing extensible quantum computing schemes, may be accomplished in part by introducing new materials with superior properties.

Van der Waals (vdW) materials - a family of layered crystals including semi-metals, insulators, semiconductors, ferromagnetic materials, superconductors, and topological insulators - can be assembled in specific arrangements to create new electronic devices called vdW heterostructures. The extraordinary and versatile electronic properties of these heterostructures, in combination with their epitaxial precision, make vdW-based devices a promising alternative for constructing key elements of novel solid-state quantum computing platforms.

We demonstrate quantum coherent control of a superconducting circuit incorporating graphene-based vdW heterostructures. We show that this device can be operated as a voltage-tunable transmon qubit, whose spectrum reflects the unique electronic properties of massless Dirac fermions traveling ballistically. In addition to the potential for advancing extensible quantum computing technology, our results represent a new approach to studying vdW materials using microwave photons in coherent quantum circuits. (arXiv:1809.05215 (2018))

This research was funded in part by the ARO grant No. W911NF-17-S-0001, and by the Department of Defense via MIT Lincoln Laboratory under AF Contract No. FA8721-05-C-0002. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the U.S. Government.

The aluminum oxide tunnel junction is one of the key components in most superconducting qubit devices. We use density functional theory to investigate the microscopic details of the junction. By using ab-initio molecular dynamics and rigorous static ground state calculations, we accurately model the details of the discrete transition of electronic structure across the tunneling interface. Significantly, the aluminum-oxygen coordination is found to vary across the junction, creating irregular potential field that is not well described by the conventional and popular models such as the Landauer–Büttiker method in a constant potential approximation. We aim to provide the atomistic, electronic details of this unique interface as described by the first-principles density functional theory to explore its non-idealities and potential sources of dissipation and loss. The ab-initio result provides a correction to a previous study on the atomic coordinations based on the reverse Monte Carlo method. The calculated work function of the oxide film of the junction was 6.2 eV compared to 4.0 eV of the aluminum metal. The atomic dipole moments are calculated using the Bader’s atoms-in-molecules method, describing the dielectric property of the junction in a microscopic detail. The defect formation energies in the vicinity of the junction interface are calculated. The diffusion property across the junction interface is assessed by the nudged elastic band method. The ab-initio calculations present further research opportunities to incorporate atomistic details into the device scale simulations of the superconducting qubits. (Prepared by LLNL under Contract DE-AC52-07NA27344.)

Electrodeposition has been used widely in the fabrication of microdevice and circuits because of the low cost, fast deposition rate, and, more importantly, the ease of scale-up. Electrodeposited superconductive films are of interest for cryogenic quantum devices as it avoids thermal perturbation resulted from the electrical heat. Such films are particularly of interest if the critical temperature (Tc) is above 4.2 K, which can be easily achieved with liquid helium. Recently, electrodeposited rhenium was demonstrated to show a critical temperature of about 6 K, representing a significant increase from its intrinsic 1.7 K[1]. However, electrodeposition of rhenium requires an acidic electrolyte, where significant hydrogen evolution is inevitable and causes inclusion of hydrogen and highly stressed or even cracked films.
On the other hand, a so-called hydration layer forms during the dissolution of salts in water. Such hydration process requires and “consumes” water molecules. When an electrolyte contains a superhigh concentration of supporting salts, for example, alkali metal salts, the hydration of such salts can deplete the free water molecules in the aqueous electrolyte and significantly mitigates the evolution of hydrogen[2,3]. This paper presents a new electrodeposition method to synthesize superconductive rhenium films using water-in-LiCl electrolyte.
A limiting current density emerged upon the addition of 5 M LiCl into an acidic Re electrolyte. This lowered hydrogen evolution reaction not only limited the voltage drop due to the high current and solution resistance, but also enabled electrochemical studies at more negative potentials. An improved film morphology was observed with a suppressed hydrogen evolution currents when the water-in-salt electrolyte was used. A critical temperature of 6 K for as-deposited rhenium film was achieved and a decrease of Tc was observed for the films upon annealing at beyond 150 C. The details of chemical uniformity, grain structures, and Tc of such Re films will be presented. In addition, attempts to electrodeposit Re alloys with this water-in-LiCl electrolyte will be discussed as well.
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2. L. Suo, O. Borodin, T. Gao, M. Olguin, J. Ho, X. Fan, C. Luo, C. Wang, and K. Xu, “Water-in-salt” electrolyte enables high-voltage aqueous lithium-ion chemistries,Science, 2015, 350(6263), 938.
3. L. Coustan, G. Shul, and D. Bélanger, Electrochemical behavior of platinum, gold and glassy carbon electrodes in water-in-salt electrolyte,Electrochemistry Communications, 2017, 77, 89.

Practical quantum computers are closer to reality than ever before. Superconducting qubits, for example, have already been integrated in arrays of ~50 qubits and can be further integrated. However, dissipation phenomena due to imperfect materials largely limit the time a qubit can store quantum information. Qubit dissipation or decoherence is mainly due to quasiparticles, flux noise, and two-level state (TLS) defects. The last are material imperfections hosted in oxidized films in proximity of on-chip superconducting devices. In this talk, we focus on TLS loss and investigate different strategies to reduce their impact on the quality of superconducting resonators and qubits.
First, we fabricate and characterize coplanar waveguide resonators made from aluminum thin films deposited on silicon substrates. We perform three different substrate surface treatments prior to aluminum deposition: One chemical treatment based on a hydrofluoric acid clean; one physical treatment consisting of a thermal annealing at 880 °C in high vacuum; one combined treatment comprising both the chemical and the physical treatments. We characterize the fabricated samples through cross-sectional tunneling electron microscopy, acquiring electron energy loss spectroscopy maps of the samples’ cross sections. We analyze the effects of the various substrate treatments on the roughness of the silicon surface by means of atomic force microscopy surface morphology mapping. We study the quality of the resonators by means of microwave measurements in the quantum regime and find that both surface treatments independently improve the resonator’s intrinsic quality factor and that the highest quality factor is obtained for the combined treatment, Q_i∼0.8 million.
We then employ similar fabrication methods as for resonators to implement superconducting Xmon transmon qubits. We characterize qubit decoherence finding energy relaxation times on the order of ~15 µs for fully flux tunable Xmons. We study the qubits by implementing one-qubit gates, while biasing the qubits using our three-dimensional wiring method, the quantum socket.
Lastly, we present the blueprints of a new type of superconducting qubit, the “pocketmon” transmon qubit. This type of qubit is a variant of the Xmon, where the qubit capacitor is realized as an almost ideal parallel-plate capacitor with vacuum as dielectric. To implement the pocketmon qubit we develop a thermocompression bonding technology, which makes it possible to fabricate multi-chip devices. The qubit is comprised of two silicon chips: The base and the cap chip. A meandered aluminum inductor and the bottom square aluminum plate of a capacitor are patterned on the base chip; the inductor is connected to a common aluminum ground plane on one end and to the capacitor through an aluminum lead on the other end. The cap chip is etched to form vacuum pockets in correspondence to the inductor, capacitor, and lead, with an aluminum square plate and a common ground plane matching those on the base chip; the top capacitor plate is connected to ground by way of an aluminum lead. The common ground plane is coated with an indium film used to bond the base and cap chip. The distance between the two capacitor plates is set to be ~10 μm. The aluminum films used to realize the capacitor plates are characterized by an ~3 nm thick native aluminum oxide film, which hosts TLS defects. However, the contribution of such films to loss is marginal if the capacitor’s plates separation is much larger than the native oxide film, as in our design. We estimate an upper bound Q_i~10⁹ for TLS loss in this device, which will be likely limited by quasiparticle loss or flux-noise.

This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund (CFREF) and the Discovery and Research Tools and Instruments Grant Programs of the Natural Sciences and Engineering Research Council of Canada (NSERC).

Low microwave loss superconducting circuit components are a necessity of fabricating high-fidelity superconducting qubits. Accordingly, significant research has focused on making high-quality planar resonators from elemental and nitride superconductors. Josephson junctions are the nonlinear component of superconducting qubits, that also need to be high performance. Interestingly, superconducting qubits all use Josephson junctions fabricated from aluminum and aluminum oxide using the double angle evaporation process. Details of this alternative design will be presented.

Plasma assisted Molecular beam epitaxy (PAMBE) is used to grow binary and ternary niobium titanium nitride alloys (Nb_xTi_1-xN) and wide bandgap nitride (AlN) superconductors. This combination of nitride materials provides sufficient degrees of freedom that synthesis of an epitaxial Josephson junction may be possible. Using a structure first approach to design optimization, the structural, surface topology, chemical characteristics, and superconducting critical temperature of these films are used for optimization of the growth conditions before resonators are fabricated and tested.

Initial growth results of nitride superconductors exhibit significant atomic interaction of the deposited adatoms and silicon substrates. Both amorphous interfacial layers, and significant diffusion of silicon during the formation of silicides are observed. Interpretation of the observed structures and impact on the superconducting properties will be discussed.

The outstanding progress in experimental quantum computing with superconducting Josephson-junction based qubits over the past few decades has pushed coherence times many orders of magnitude above that of the first measured. We are also in the midst of scaling towards complex architectures of multi-qubit processors where maintaining very low gate error rates at the limits supported by coherence times is extremely important. Here we will review some of the critical materials and device challenges for superconducting qubits from the perspective of improved coherence and improved error rates. Furthermore, we will discuss traditional validation and verification techniques, while also discussing alternatives to benchmark the performance of small quantum processors for near-term applications.

Two-level state (TLS) loss in dielectric materials and interfaces remains at the forefront of materials research in quantum information science. Due to a lack of defects and decreased disorder, crystalline films grown epitaxially in an ultrahigh vacuum environment are thought to have a reduced TLS concentration and thus lower loss at millikelvin temperatures and single photon powers [1]. In this work, we demonstrate a method of sensitive and accurate TLS loss measurement by measuring a lumped element resonator fabricated from a superconductor-dielectric-superconductor trilayer. The deposition of the trilayer prior to fabrication increases control over the metal-dielectric interfaces, and the generalized fabrication process allows straightforward comparison of dielectrics that are of interest to quantum computing. We extract the dielectric loss by comparing to coplanar waveguide resonators and lumped element resonators with interdigitated capacitors. This method is designed to compare dielectric loss in both epitaxial and non-epitaxial trilayers.

[1] Gao, J. The Physics of Superconducting Microwave Resonators. Thesis (2008).

Superconducting quantum computing architectures rely on resonators and qubits with coherence lifetimes that are limited by two-level systems (TLS) present in bulk and interfacial dielectrics. Understanding this source of loss is critical to improving performance in superconducting circuits. However, few techniques exist for characterizing material losses under conditions relevant to superconducting quantum circuit operation. In this work, we present a method for quantifying the TLS losses of different bulk and interfacial dielectrics present in superconducting coplanar waveguide (CPW) resonators. By combining statistical characterization of sets of specifically designed CPW resonators on isotropically etched silicon substrates with detailed electromagnetic modeling, we determine the separate loss contributions from individual material interfaces and bulk dielectrics. Additionally, we report on progress towards applying this technique to characterize and improve qubit losses. In general, this technique provides an effective method for assessing superconducting qubit materials in order to guide targeted improvements to qubits, resonators, and their superconducting fabrication processes.

This material is based upon work supported in part by the Intelligence Advanced Research Projects Activity (IARPA) and in part by the Department of Defense under Air Force Contract No. FA8721-05-C-0002 and/or FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of IARPA, the Department of Defense, or the US Government.

Superconducting qubits have made admirable improvements in performance and scaling over the past decade. However, much of that progress has been made by circumventing the issues associated with loss in the single photon regime by simply removing interfaces near qubits. I will introduce the mechanism of energy loss due to two-level system and share several leading candidates for microscopic structural origin of these parasitics. I will highlight the need for orthogonal metrology techniques and better theoretical understanding of our material systems at the energy and temperature scales at which they operate. Lastly, I will share recent efforts to create a standardized testbed for characterizing loss in hopes of getting more uniform measurements and facilitating translation from materials research to quantum device engineering.

Uniquely characterizing loss from two-level systems (TLS) at metal-substrate, metal-air, and substrate-air interfaces and in a dielectric substrate is challenging due to the nearly proportional scaling of the dielectric participations in response to changes in geometry and anisotropic trench depth. We developed a technique utilizing isotropic etching to assign a specific loss tangent to each dielectric, and use that to determine the dominant dielectric losses for a specific fabrication process, enabling targeted geometry and process changes to maximize performance. In this talk, we characterize the loss from high quality factor resonators (Qi>1M) for aluminum, titanium nitride, and niobium, and demonstrate the technique’s application by targeting specific defect layers to alter the dielectric losses specifically from these defect layers.
This material is based upon work supported in part by the Intelligence Advanced Research Projects Activity (IARPA) and in part by the Department of Defense under Air Force Contract No. FA8721-05-C-0002 and/or FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of IARPA, the Department of Defense, or the US Government.

Two-level systems (TLS) are one of the major sources of loss of information in superconducting qubits. At single photon energy, the superconducting waveguides lose energy via resonant interaction of its electric field with TLS defects that are generally present at various surfaces and interfaces. In general, TLSs are present at the metal-substrate, substrate-vacuum and vacuum-metal interfaces. The chemical species of these TLSs can vary due to the variation in the constituent materials and fabrication residues. Using an electric field participation model, the measured quality factor of the resonators can be related to the loss tangent (tan(δ_i)) associated with TLSs by Σ_i p_i tan(δ_i) = Q_TLS^-1 where p_i is the participation ratio of the electric field which is the fraction of the total electric energy stored at each interface.
In this study, the role of different chemical species at various interfaces of the coplanar waveguide resonators are investigated. Quarter-wavelength coplanar waveguide resonators are fabricated from MBE grown aluminum (Al) on silicon (Si (111)) wafers. Resonators are wet-etched to ensure that the devices are as identical as possible. Devices are packaged and measured consistently to reduce any other sources of variation in the measured quality factor. Variations in the surfaces are introduced by distinct treatments on Si and Al surfaces that allow comparison of interfaces with different incorporation values of oxygen and nitrogen. These surface treatments also modify the structural properties of the overgrown Al showing polycrystalline, twinned single crystal, and pure single crystal Al films.
These treatments of the Si and Al surfaces impact the measured quality factor. The low loss devices have single photon internal quality factor near 800k. The measured data along with the simulated participation ratio is used to calculate the relative loss tangent across the tested interfaces. The relation between the calculated loss tangent and the various chemical species present at interfaces will also be explored.

A continuous taper can be engineered between two tranmission lines of different characteristic impedance to reduce reflection of the signal that propagates from one line to the other, There are a number of taper designs presented in the literature that achieve this goal. [1,2] These designs assume impedance mismatch of the two lines is sufficiently small that voltage reflections within the taper also can be considered small. Here we extend the theory of the optimal lossless impedance taper of [2], allowing for impedance mismatch and taper voltage reflection of arbitrary magnitude. We apply our extended theory to the optimal design of taper for the two use cases of (i) an unavoidably large impedance mismatch between transmission lines and (ii) a narrow notch filter corresponding to a specific range of frequencies of bandpass. We also apply our theory to a proposed design of on-chip Purcell filter, which can be used in the fast readout of superconducting transmon and Xmon qubits, for example.

* This work was supported by the NIST Quantum Initiative. RPE acknowledges grant 70NANB17H033 from the US Department of Commerce, NIST.

[1] R. W. Klopfenstein, Proc. of the IRE, 31 (1956); D. M. Pozar, Microwave Engineering, 4th ed. (J. Wiley & Sons, New York, 2012) pp. 261-267.
[2] R. P. Erickson, J. of Appl. Physics. 123, 074501 (2018).

The 2D Kitaev model on a honeycomb lattice predicts a special quantum spin liquid (QSL) ground state with excitations resembling Majorana Fermions and gauge flux excitations. These emergent features are exciting prospects to both basic physics and applications towards technologies for topologically protected quantum qubits. Our past range of experiments on the 2D magnetic Mott insulator alpha-RuCl3, which has honeycomb layers held together with weak van-der-Waals interactions, have revealed a continuum of fractionalized excitations resembling predictions from Majorana Fermions. In a 8 T magnetic field, the long-range order vanishes and the continuum becomes gapped, supporting a state where direct evidence of non-Abelian excitations can be measured. Interestingly, within this 8 T phase, recent thermal Hall effect measurements have revealed 1/2-quantized chiral edge states reminiscent of free Majorana Fermions stable to 5 K, producing a lot of excitement in the community. In this talk, I will describe our recent neutron experiments on the role of the 3D magnetic long-range order and the nature of the 2D stacking, which is critical to understand this material and its phases. Our result point to the hierarchy of the 2D (within a 2D layer) and 3D interactions (between the 2D layers) in the Hamiltonian which is responsible for the physics observed. I will describe the present and future endeavors to complete the understanding of the phase diagram of this material, as well as on how to stabilize the phase where these excitations are observed.

Understanding the detailed materials origins of decoherence in qubit devices will enable rational design of improved devices and fabrication processes for practical quantum information processing. We utilize first principles materials simulations to study a range of possible coherence-limiting defects and materials properties at the atomic scale. Examples will be presented for superconducting qubits, ion trap qubits, and silicon/silicon-germanium quantum dot qubits.

Specifically, we will review our recent work in the computational search for sources of flux and dielectric noise in superconducting qubits, including paramagnetic surface impurities, grain boundary effects, the atomic structure of Josephson junction dielectric layers, and the dielectric response of interface features. Many of these atomic features are associated with spurious two-level fluctuators that couple to the qubit and cause decoherence. For ion traps, possible sources of anomalous heating associated with electrode materials and surface impurities are studied with atomistic simulations. The phenomenon of anomalous motional heating of the trapped ion is a major limiting factor of the coherence time for surface ion trap devices. Various levels of detail are used to model the surfaces and impurities realistically. Finally, we will describe studies of dangling bond defects in insulating layers of silicon and silicon-germanium quantum dot devices as a possible source of charge noise in those devices. Prepared by LLNL under Contract DE-AC52-07NA27344.

Cooling samples to cryogenic temperatures is common for quantum materials and quantum information devices. Effective cooling requires adequate thermal conduction between the cooling stage and the sample; however, many mounting techniques introduce materials with mismatched coefficient of thermal expansion. The mismatch may result in a bending moment or stress in the sample. Both can deform the sample while measurements occur, may cause plastic deformation, and potentially couple to the physical quantity of interest.

In this study, various mounting techniques are employed to create thermal conduction pathways between the cooling stage and the sample. A three-tiered structure of CTE mismatch (sample/mounting material/stage) is studied. Silicon wafers are good standard reference samples widely used across thin film research, are flat and mirror-like surfaces that will reflect a laser signal. The curvature of a Si wafer sample is measured in real time as a function of temperature. A projected pattern of laser spots is reflected from a piece of Si wafer that is mounted to a stage in a cryostat. Monitoring changes in the spot spacing is a result of the sample’s change in curvature and indicates an applied bending moment. Mounting techniques tested include using common cryogenic adhesives such as Apiezon N grease, GE varnish and Stycast epoxy as well as strapping samples in place on a copper cooling stage with copper wire and Teflon tape. Finally, the Cu sample stage is replaced with a Si sample stage in order to match the CTEs of the stage and the sample, leaving only the mismatch of a thin bonding layer. These techniques are compared and analyzed using a balanced force model and linear elastic/plastic theory to determine the degree to which each method stresses the sample.

In situ electron microscopy can be used to reveal the correlation between local atomic structure and properties. This talk will address in situ electron microscopy using local sample manipulation combined with the ability to measure the local electrical transport properties and effects induced by electric fields, light and mechanical strain. This is achieved by using a scanning tunnelling microscope in scanning electron microscopes and transmission electron microscopes [1-4] and by specially designed stages for uniaxial mechanical strain [5]. The electron microscopes provide both imaging capabilities and spectroscopy methods for the determination of local material and electronic structure. The use of scanning electron and transmission electron microscopes enables the in situ studies to be carried out on different length scales spanning from the subatomic dimension to micrometer. The position of individual atoms and atom columns can be determined with picometer precision [6]. The direct correlation on the small scale involving individual interfaces, defects and atoms provides access to new information about which microstructural constituents that are active in determining the material properties on the different length scales. It is possible to study both bulk and surface effects and understand how the properties can be tuned and the performance tailored for each specific application.

[1] Y. Jompol, H. Olin and E. Olsson, Rev. Sci. Instr. 74, 4945 (2003).
[2] K. Svensson, H. Olin and E. Olsson, Phys. Rev. Lett. 93 (2004) 14590.
[3] H.M. Nilsson, L. de Knoop, J. Cumings and E. Olsson, Carbon, 113, 340 (2017).
[4] L. de Knoop, M.J. Kuisma, J. Löfgren, K. Lodewijks, M. Thuvander, P. Erhart, A. Dmitriev and E. Olsson, Phys. Rev. Mat. 2018, DOI: 10.1103/PhysRevMaterials.00.005000.
[5] L. J. Zeng, C. Gammer, B. Ozdol, T. Nordqvist, J. Nygård, P. Krogstrup, A.M. Minor, W. Jäger and E. Olsson, Nano Letters 2018, DOI:10.1021/acs.nanolett.
[6] T. Nilsson Pingel, M. Jørgensen, A.B. Yankovich, H. Grönbeck and E. Olsson, Nature Communications 2018, DOI: 10.1038/s41467-018-05055-1.

The first quantum revolution provided a microscopic understanding of nature and underpinned the development of transistors, originally made in germanium. The following assembly of silicon transistors into integrated circuits triggered the digital age, which completely changed our daily life. We are now in the midst of the second quantum revolution, in which quantum matter is engineered to develop disruptive technologies beyond the reach of classical understanding. Quantum computing is considered by many the man on the moon goal of such second quantum revolution.

How will we get there?

Group-IV semiconductors Si and Ge offer several advantages for the realisation of spin quantum bits. Si and Ge can be isotopically purified into a nuclear spin free materials, which allows long spin coherence time. In this talk I will discuss, from a materials perspective, how we are turning everyday silicon or germanium into the quantum computing wonder material by using quantum dots defined electrostatically in SiGe heterostructures. A quantum dot defined by metallic gates in a strained SiGe heterostructure can trap a single electron or hole, such that the electron or hole spin can be operated as a quantum bit, the elementary unit of quantum computation.
Electron quantum dots in Si/SiGe heterostructure are promising because bear similarities from a materials and integration perspective to the transistors used in advanced semiconductor manufacturing. Hole quantum dots in Ge/SiGe heterostructures are a complementary option for fast quantum hardware due to the different band structure properties of Ge compared to Si.

To deploy a qubit into high volume manufacturing in a quantum computer requires stringent control over substrate uniformity and quality. In this talk we will focus on carrier mobility and energetic valley splittings in SiGe heterostructures, which are two key electrical metrics of substrate quality relevant for qubits. and correlate them to structural quality of the heterostructures. To ensure rapid progress in quantum wells quality we have implemented fast feedback loops from materials growth, to innovative heterostructure FET fabrication, and low temperature characterisation. In this direction we show progress in developing a cryogenic platform for high-throughput magnetotransport measurements.

One promising technology for creating a quantum computer is silicon germanium (SiGe) quantum dots. This approach confines electrons electrostatically in a buried Si quantum well (QW) and encodes information on specific quantum states of the electron. For success, the material must be a high-quality single crystal with atomically abrupt interfaces between the QW and the barrier, have a well-controlled QW thickness, and low background impurity concentrations.
Alternatively, holes confined in a Ge QW has high interest because strain can produce a single valence band state that does not suffer from valley degeneracy like electrons in the conduction band of Si. Compressively strained Ge is desired to lift the degeneracy between the heavy hole (HH) and light hole (LH) bands such that the participating holes occupy only the ground state of the HH band that exhibits a light effective mass. The Ge QW is compressively strained by growing on a relaxed Si_0.2Ge_0.8 buffer layer that cannot be grown on Si or Ge substrates; rather it must be grown on a relaxed Si_0.2Ge_0.8 virtual substrate. Demonstrations using RP-CVD have used a thick Ge layer grown directly on Si (001) that is combined with a reverse composition grading to Si_0.2Ge_0.8 [1]. These virtual substrates usually possess a rough surface and crosshatch morphology that needs chemical mechanical polishing before QW growth.
This experimental study focuses on the growth and characterization of abrupt metamorphic Si_0.2Ge_0.8 buffer layers grown on Si (001) substrates by means of MBE. The Si and Ge fluxes are created with electron beam evaporation solid sources that are controlled by electron impact emission spectroscopy. In this proposed design, a fully relaxed Si_0.2Ge_0.8 layer is directly grown on Si (001) at a lower substrate temperature than what can be accomplished with RP-CVD. A strain balanced Ge/Si_0.4Ge_0.6 supper lattice is grown to filter threading dislocations followed by a relaxed Si_0.2Ge_0.8 spacer that also serves as the bottom barrier for the Ge QW. The 10 nm-thick Ge QW is grown with a Si_0.2Ge_0.8 top barrier layer and a 1-nm Si cap. Growth details and structural characterization of the materials using a variety of techniques will be described.

1. V. A. Shah, et.al., J. Appl. Phys, 107, 064304 (2010)

Germanium is arguably the oldest semiconducting material used for electronics. Thanks to significant progress in material growth and accompanying developments in device engineering, germanium is re-emerging as a competitive next-generation material for beyond Moore’s law computing paradigms, specifically spintronics and quantum information schemes. Among various germanium-based materials, silicon-germanium epitaxy on top of silicon wafers results in silicon foundry compatible materials and holds great promise in manufacturability. In strained germanium quantum wells sandwiched between relaxed silicon-germanium layers, two-dimensional hole gases (2DHGs) with mobilities exceeding 10⁵ cm²V^-1s^-1 at cryogenic temperatures can now be routinely achieved by a handful of groups. This high mobility and the potential compatibility with the silicon industry make germanium quantum wells a promising material platform for exploring quantum applications.
Pursuing new applications using holes in germanium requires a comprehensive understanding of the quantum electronic properties of these carriers. To this end, we have designed and grown strained germanium quantum well structures using chemical vapor deposition, developed fabrication processes for inducing 2DHGs in these undoped quantum wells, and carefully measured and extracted the effective mass, g-factor, spin-orbit coupling strength, scattering rate, and dephasing rate as a function of the carrier density through magneto-transport experiments. In this presentation, we will report our measurements and findings. In particular, the in-plane effective mass remains roughly constant at ~0.08 of the bare electron mass over a wide density range. The out-of-plane g-factor increases strongly with decreasing density, while the in-plane g factor is small and only weakly density dependent. The spin-orbit coupling is consistent with being of the cubic Rashba type and is highly tunable. We also discuss the numerical approach we developed for extracting the spin-orbit coupling constant from weak anti-localization beyond the usual diffusive transport regime, where conventional models fail. Last, we will discuss practical considerations of non-equilibrium charge distribution in these germanium quantum wells at cryogenic temperatures.
Based on our developed materials and processing capabilities, we have designed, fabricated, and tested single and double quantum dots with single and multiple metal gate layers. We will present our results in quantum dot measurements and three-dimensional modeling of these quantum dot structures, including the spin-orbit coupling effects on energetics.
This work was partly supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) and partly by the Laboratory Directed Research and Development Program at Sandia National Laboratories. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. DOE, Office of Basic Energy Sciences, user facility. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE's National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the United States Government. The work at National Taiwan University was supported by the Ministry of Science and Technology under the contract 106-2112-M-002-009- and the Ministry of Education through the Higher Education Sprout Projects (career development project: NTU-107L7818 and NTU core consortium: 107L891702).

We report on magnetotransport of gated Hall bar devices fabricated on isotopically enriched ²⁸Si epi-layers and natural abundance Si on the same Si substrate. Isotopically enriched ²⁸Si is regarded as an ideal environment for quantum computation (QC) as the elimination of unpaired nuclear spins can result in low error rates for QC. Using a mass selected ion beam deposition technique, we have developed a method to grow epitaxial ²⁸Si, and routinely achieve better than ²⁸Si isotope fractions. A unique advantage of this technique is that the ability to control the level of enrichment from natural abundance to highest possible enrichment of ²⁸Si enabling targeted enrichment. The magnetoresistance measurements of devices fabricated on ²⁸Si and ^nat.Si at at 2 K, show maximum mobilities of and at an electron density of , respectively. For , both types of devices demonstrate well developed Shubnikov-de Haas oscillations on the longitudinal magnetoresistance. However, the device fabricated on isotopically enriched ²⁸Si also shows a (relatively) stronger weak-localization behavior. Using the dependence of weak-localization and Shubnikov-de Haas oscillations, we deduce the background impurity scattering and interface roughness scattering to be the dominant scattering mechanisms in these devices. We believe that the lower mobility and stronger weak-localization observed for the devices fabricated on ²⁸Si is due to dilute adventitious C, N and O detected in ²⁸Si.

Deterministic dopant placement methods enable atom-based structures with applications ranging from novel low dimensional quantum materials to devices for quantum information processing. Placement of individual dopant atoms in the Si lattice with high precision is achieved using hydrogen-based scanning probe lithography. This technique enables fabrication of atomically thin, monolayer dopant profiles with extremely high density and abrupt interfaces. Controlling the position and electronic state of deterministically placed atoms in a solid-state environment allows a quantitative understanding of single-atom-based phenomena and enables devices to reach the single atom limit.

Functionality and repeatability of atom-based devices depend greatly on controlling the material properties at the atomic scale including cleanliness, near perfect atomic order, dopant layer confinement and low-temperature epitaxial silicon overgrowth. Material imperfections such as defects and contaminants can cause instabilities in quantum device operation. We present a complete fabrication process for the creation of robust nano and atomic scale devices with atomically aligned gates and contact pads on clean silicon surfaces in an ultrahigh vacuum environment (10^-11 Torr) using a scanning tunneling microscope (STM). By optimizing epitaxial growth techniques and using locking layers we enhance the confinement of Phosphorus dopant atoms, enabling improved systematic performance of single electron and single or few atom quantum devices. We will discuss low temperature transport measurements of atomic-scale tunnel junctions and single electron transistors that demonstrate stable coulomb blockade oscillations. The device stability is the direct result of controlling materials and process conditions at the atomic scale.