Symposium EM1 : Materials Issues for Quantum Computing

Extremely long electron and nuclear spin coherence times have recently been demonstrated in isotopically pure Si-28 [1,2] making silicon one of the most promising semiconductor materials for spin based quantum information. The two level spin state of single electrons bound to shallow phosphorus donors in silicon in particular provide well defined, reproducible qubits [3] and represent a promising system for a scalable quantum computer in silicon. An important challenge in these systems is the realisation of an architecture, where we can position donors within a crystalline environment with approx. 20-50nm separation, individually address each donor, manipulate the electron spins using ESR techniques and read-out their spin states.

We have developed a unique fabrication strategy for a scalable quantum computer in silicon using scanning tunneling microscope hydrogen lithography to precisely position individual P donors in a Si crystal [4] aligned with nanoscale precision to local control gates [5] necessary to initialize, manipulate, and read-out the spin states [6]. During this talk I will focus on demonstrating spin transport [7] and single-shot spin read-out of precisely-positioned P donors in Si. I will also describe our approaches to scale up using rf reflectometry [8] and the investigation of 3D architectures for implementation of the surface code [9].

[1] K. Saeedi et al., Science 342, 130 (2013).
[2] J. T. Muhonen et al., Nature Nanotechnology 9, 986 (2014).
[3] B.E. Kane, Nature 393, 133 (1998).
[4] M. Fuechsle et al., Nature Nanotechnology 7, 242 (2012).
[5] B. Weber et al., Science 335, 6064 (2012).
[6] H. Buch et al., Nature Communications 4, 2017 (2013).
[7] B. Weber et al., Nature Nanotechnology 9, 430 (2014).
[8] M.G. House et al., Nature Communications 6, 8848 (2015)
[9] C. Hill et al., Science Advances 1, e1500707 (2015).

Hydrogen Depassivation Lithography (HDL) using a Scanning Tunnelling Microscope(STM) has been used to create atomic-precision patterns for Phosphorus-dopant-based quantum devices. In order to transfer the pattern into dopants, the surface is exposed to phosphine (PH₃), and then a brief anneal to 350°C or 500°C is performed to trigger the exchange of a surface P atom with a Si dimer atom. For devices such as the ‘single atom transistor’ [1] or for spin qubits, a single isolated P atom is incorporated into the surface at a precise distance from other electrodes. In this case, a 3-dimer pattern is created, into which three PH₃ molecules are adsorbed. The anneal process drives off two of these, and the third incorporates into the Si surface. However, three issues remain with the current process. First, the yield of single P atom incorporation is only around 70% for a 3-dimer pattern; with larger patterns, the yield increases to 100%, but it then becomes possible for 2 P atoms to be incorporated. Second, the exact position of the P atom cannot be controlled within the pattern. Finally, since the anneal process may damage the patterning, inspection of the incorporation anneal is difficult, and error correction is almost impossible.
With our ZyVector STM control system we are able to write over the same area repeatedly, as we have demonstrated using disilane to grow multiple atomic layers of Si in patterned areas of a Si(001):H surface[2]. Making use of this improved position control, we have developed a tip-assisted process for P incorporation. Recently, a group showed that the PH₂+H to P+3H reaction could be driven by an STM tip at room temperature [3]. We present STM data at elevated temperatures on PH₃-saturated Si(001) surfaces and in PH₃ patterned areas of H-terminated Si(001) surfaces. We confirm that H can be removed from the adsorbed PH₃ fragments, and further, show that the P incorporation reaction can be activated by an STM tip at a temperature (ca. 200°C) where background PH₃ fragments and H are stable, as demonstrated by the formation of short Si islands similar to those obtained from a 350°C anneal process.
Scaling this down to the single P atom case, it should be possible to create a single-dimer pattern, adsorb one PH₃ molecule, remove a minimal number of H atoms around it, and thus drive adsorption into a more deterministic position. A number of other potential applications of this process can be imagined, including a double-doping process, to boost the P density past the 0.25 ML single-dose limit, and even low-temperature encapsulation using Patterned ALE.

1: M. Fuechsle, J. A. Miwa, S. Mahapatra, H. Ryu, S. Lee, O. Warschkow, L. C. L. Hollenberg, G. Klimeck, and M. Y. Simmons Nat Nano 7 242-246 (2012)
2: J. H. G. Owen, J. Ballard, J. N. Randall, J. Alexander, and J. R. Von Ehr J. Vac. Sci. Technol. B 29 06F201 (2011)
3: Q. Liu, Y. Lei, X. Shao, F. Ming, H. Xu, K. Wang and X. Xiao Nanotechnology 27 135704 (2016)

Moore’s law extrapolates to microelectronic devices with atomic size features around 2020 [1]. Anticipating engineering of nanoelectronics at this scale, techniques to tune dopant profiles in silicon have evolved to the ultimate limit of single-atom control. A single atom transistor [2], a device with just one P dopant atom placed in the channel with atomic selectivity, was recently fabricated via hydrogen resist scanning tunneling microscopy (STM) lithography. Despite the promise of atomically precise dopant placement, there are significant challenges to fabrication based on STM lithography such as scale-up, robustness, yield, and reproducibility.

This talk describes techniques to evaluate and optimize the yield and reproducibility of patterning and incorporation for single dopant placement. The hydrogen resist STM lithography method uses electrons from the STM tip to selectively desorb hydrogen atoms from the Si(100) – 2×1:H surface. Dosing the sample with PH₃ and annealing selectively incorporates P dopants into the regions patterned with the STM tip. The key challenges for fabricating the dopant arrays are alignment of the STM tip to the dimer rows of the Si(100) surface, choice of lithographic window size and patterning conditions, and identification of the incorporated dopant after dosing and annealing the sample. Scaling the arrays to larger sizes requires reproducible STM tips that pattern consistently and very low alignment error. Using the precise alignment of the STM tip to the dimer rows of Si(100) surface, we have improved lithography yield for patterning windows for single dopant incorporation from 10% to 40%. We have developed image analysis capability to rapidly identify the dopant atoms in order to verify the results of the array fabrication and provide feedback to the lithography and dosing conditions for process optimization. Comparing results of dopant incorporation with modeling enables fine tuning of the PH₃ dosing and incorporation conditions to improve the single dopant yield.

This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. Data collected using a ZyVector™ STM Lithography Control System from Zyvex Labs.

[1] International Technology Roadmap for Semiconductors, http://www.itrs2.net/.
[2] Fueschle, et al., Nat. Nano. 7(4), 242 (2012).

Quantum computers that exploit the nature of quantum physics have the potential to solve some problems much more efficiently than classical computers can. Motivated by the tremendous scalability of classical silicon electronics, we are working to build a large-scale quantum computer using silicon technology similar to that used to build current classical computers, specifically, electrically-gated quantum dots in silicon-germanium heterostructures. This talk will discuss the fundamental physics and materials science challenges that arise, and how close coupling between theory and experiment has enabled substantial progress towards the goal of high fidelity qubits. Prospects for further development will also be discussed.

Nanoscale lithographic control of both donors and acceptors in Si are of great interest to push the limits of device size, fabricate qubits, and create locally delta doped regions. Phosphine has been established as a viable source for donor doping of Si with atomic precision [1], but a corresponding process for acceptor doping has proved challenging.
We use scanning tunneling microscopy combined with hydrogen lithography to create and characterize nanoscale acceptor doped regions on the Si(001) surface. On an n-type hydrogen passivated Si(001) sample, arrays of dangling bonds are lithographically defined by the STM tip and then exposed to diborane delivered through a capillary doser, which leads to an enhanced local pressure at the tip-sample junction. Another related process is also explored, in which the pattern writing occurs concurrently with diborane exposure. Tunneling spectra confirm incorporation of dopants occurs through the observation of p-type behavior in the lithographically defined regions in an otherwise n-type Si sample. We explore how substrate temperature and lithography conditions affect dopant incorporation.
We also present a novel method for producing diborane through use of a CVD precursor, Hf(BH₄)₄, that has utility for writing both nanoscale metallic and p-type doped regions. It was developed as a carbon-free CVD precursor for deposition of films of metallic HfB₂ [2-3], and it has been used for STM lithography of nanoscale metallic features [4]. Here we heat the precursor prior to introducing it to the analysis chamber, such that only the resulting diborane and hydrogen reach the sample.

We acknowledge valuable discussions regarding this work with Dr. J. Randall and Dr. J. Owen at Zyvex Labs and with Dr. Peter Scherpelz at the University of Chicago.

[1] S. R. Schofield et al. Physical Review Letters 91(13) 136104 (2003).
[2] J. Jensen et al. Journal of the American Chemical Society 110 1643-1644 (1988).
[3] S. Jayaraman et al. Journal of Vacuum Science and Technology A 23(6) 1619-625 (2005).
[4] W. Ye et al. ACS Nano 4(11) 1618-1624 (2010).

Recently, quantum dots (QDs) and double quantum dots (DQDs) have been well-studied which is motivated by the desire to understand quantum mechanical systems using electron spin or the charge states. These efforts are now applied to a solid-state-based quantum bit (qubit) and demonstrate full control of single spin-qubit in DQDs with the structure which generate magnetic field for electron spin resonance (ESR) [1]. Extending double QDs to triple QDs (TQDs) is essential toward controlling and understanding the multi-spin properties. Furthermore, from the standpoint of qubits, it also provides a simple scheme to single-qubit manipulation, which removes the need of the structure for ESR. TQDs qubits are successfully made in III–V semiconductors [2], however, the coherence of electron spins in these materials is limited by hyperfine interactions with nuclear spins. From the perspective of materials, silicon TQDs are ideal for qubits because long coherence time attributed to its isotopes with zero nuclear spin is expected. However, in silicon, it is relatively difficult to observe the few-electron regime because of the large electron effective mass in silicon compared to the other compound semiconductor materials. Therefore, the research of silicon TQDs have not been fully established despite the advantages.
Here we report fabrication of physically-defined TQD, observation of the few-electron regime and equivalent-circuit simulation of their charge stability diagram. In this study, we formed TQDs (the diameter of each quantum dot is ~40nm), a charge sensor (CS) and several side gates on 35-nm-thick silicon-on-insulator (SOI) by electron beam lithography and SF₆ dry etching [3]. In order to induce two-dimensional electron gas and obtain an Ohmic contact with each electrode, we fabricated metal-oxide-semiconductor (MOS) structure composed of gate insulator (~60-nm-thick SiO₂) and top gate (~200-nm-thick poly-silicon). By measuring the device with applying voltages to side gates (V_SGR and V_SGL) at a temperature of 300 mK, we successfully observed the few-electron regime in triple quantum dots. Moreover, we simulate the charge stability diagram with equivalent-circuit model composed of capacitors and tunnel barriers modeled as resistors and capacitors in parallel. The equivalent-circuit simulation makes it clear that we can successfully locate three QDs in series and side-gates are coupling to each QDs as planned. It means that we prepare the ideal environment for spin manipulation toward the realization of TQD-based electron spin qubits.
This work was financially supported by Kakenhi Grants-in-Aid (Nos. 26709023, 26630151 and 26249048) and the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

[1] J. R. Petta, et al., Science 309, 2180(2005)
[2] E. A. Laird, et al., Phys. Rev. B 76, 075306(2007)
[3] K. Horibe et al., Appl. Phys. Lett. 106, 083111 (2015)

We demonstrate a 12 quantum dot device fabricated on an undoped Si/SiGe heterostructure as a proof-of-concept for a scalable, linear gate architecture for semiconductor quantum dots. The device consists of nine quantum dots in a linear array and three single quantum dot charge sensors. We show reproducible single quantum dot charging and orbital energies, with standard deviations less than 20% relative to the mean across the nine dot array. The single quantum dot charge sensors have a charge sensitivity of 8.2×10^-4 e/ and allow the investigation of real-time charge dynamics. As a demonstration of the versatility of this device, we use single-shot readout to measure a spin relaxation time T₁ = 170 ms at a magnetic field B = 1 T. By reconfiguring the device, we form two capacitively coupled double quantum dots and extract a mutual charging energy of 200 µeV, which indicates that 50 GHz two-qubit gate operation speeds are feasible.

Defects in wide-band-gap semiconductors have emerged as promising single-photon emitters and solid-state qubits. The nitrogen-vacancy (NV) center in diamond has been widely studied as an individually-addressable quantum system that can be initialized, manipulated, and measured with high fidelity at room temperature. The success of the NV center stems from its nature as a localized “deep-center” point defect. We have performed in-depth analyses of the NV center, using cutting-edge first-principles techniques, in order to elucidate its properties and to predict which centers in other materials might exhibit similarly favorable properties. I will present an overview of the physics of deep centers, focusing on the characteristics that are key to the performance as “NV-like” centers [1,2]. We have the capability to predict transition energies and lineshapes associated with the optical transitions that play a central role in the functionality of the defect. Our methodology rigorously addresses the coupling between electrons and phonons during an optical transition [3]. We obtain an excellent description of the luminescence band, including all key parameters such as the Huang-Rhys factor, the Debye-Waller factor, and the frequency of the dominant phonon mode [4].

Work performed in collaboration with A. Alkauskas, D. Awschalom, L. Gordon, A. Janotti, J. Varley, and J. Weber, and supported by DOE and NSF.

[1] L. Gordon, J. R. Weber, J. B. Varley, A. Janotti, D. D. Awschalom, and C. G. Van de Walle, MRS Bull. 38, 802 (2013).
[2] J. B. Varley, A. Janotti, and C. G. Van de Walle, Phys. Rev. B 93, 161201 (2016).
[3] A. Alkauskas, J. L. Lyons, D. Steiauf, and C. G. Van de Walle, Phys. Rev. Lett. 109, 267401 (2012).
[4] A. Alkauskas, B. B. Buckley, D. D. Awschalom, and C. G. Van de Walle, New J. Phys. 16, 073026 (2014).

The advancement of diamond quantum technologies will require better analytical techniques to probe the distribution of dopant atoms in these materials. To achieve optical addressing of individual spins, the dopant levels in the materials must be quite low, consequently traditional nano-analytical techniques such as STEM-EELS and STEM-EDS cannot directly provide the required chemical sensitivity to understand dopant distributions in these materials, however correlative techniques are a solution.
Practical quantum technologies built from wide band gap semiconductors, in particular diamond and silicon carbide, have become realistic thanks to careful defect engineering of these materials. Color centers, created by point defect dopant atoms, such as silicon and nitrogen, are the basis for nanomagnetomers that can sense and measure the state of a single nuclear spin and provide a platform for the entanglement of macroscopically separated spin states.
Local electrode atom probe tomography (LEAP) provides 3D spatiochemical mapping with elemental sensitivity down to 1 ppm and sub nm spatial resolution. Recently, LEAP has proven invaluable for analyzing dopant concentrations in FIN-FETs, where the 3D doping profile is critical to the performance of the devices and there may be only a handful of dopant atoms per structure. Single crystal CVD grown diamonds were prepared and the classical lift-out method has been used to produce APT samples. Experiments were performed in a LEAP 4000X HR system with conditions of acquisition: 60-80 pJ, 100 kHz, 50 K, DR: 0.2-0.5%. The presence of carbon clusters up to C₂₀ is currently observed in the mass spectra. However, these specific conditions of sample preparation and acquisition allow collecting a few millions of atoms before fracture of the sample, and thus allow a relatively decent reconstruction of the diamond sample, the dopant locations can then be mapped directly onto correlated HAADF STEM imaging.
Atom probe tomography of diamond remains challenging due to the low conductivity and large band gap of the material, however the insights into dopant clustering and local dopant environment could provide information regarding the selection of growth, doping, and processing parameters, consequently leading to better materials and hence better devices, the correlation of APT and TEM/STEM information has shown a path forward to provide a practical method for high resolution analysis.

The study of optically active defects in diamond, known as colour centres, has attracted increasing interest in the last few years in a wide range of applications, mainly quantum information processing. Particularly, the SiV colour centre has been highlighted as a promising photon source among other colour centres in diamond, due to its interesting optical properties at room temperature.

SiV colour centres acting as single photon emitters can be created through different approaches in in-situ Chemical Vapour Deposition growth (CVD). Either by introducing silicon as a solid source or in a gas phase using silicon containing gases such as silane. However, the introduction of silicon as a solid source results in an uncontrolled silicon doping and therefore little control over the optical properties of the defect created.
To overcome these drawbacks, silane was added into the main H₂-CH₄ CVD growth gas process. Different diamond films with changing silane concentration were grown. Scanning Electron Microscope, Raman spectroscopy, Photoluminescence (PL) and Secondary ion mass spectrometry measurements were performed to determine the optimal silane concentration to achieve high PL intensity.
For quantum applications however the development of a controllable photon source and hence a suitable SiV positioning method is desirable. For this aim diamond nanoparticles with custom colour centres were also produced from the diamond films following a milling strategy.
Differences in photoluminescence properties on both diamond films and diamond nanoparticles will be shown.

Diamond is famous for its exceptional properties like extreme hardness, high refractive index, and record thermal conductivity. That’s why applications of diamond cover a huge and ever growing field. In this talk I will focus on exceptional optical and spin properties associated with single impurity atoms in diamond crystal. Such defects have been identified as a prominent candidate for quantum technologies. Having single atom doping process and technique allowing to engineer isotopic composition of diamond lattice at hand, we explore electron and nuclear spins of single atoms for quantum applications. First experiments towards realization of quantum simulator based on coupled nuclear spins in diamond will be presented.

The rapidly growing interest in quantum-information technologies has created a need for identifying optically addressable single-spin centers that may serve as qubits. Here we investigate point defects and defect complexes in AlN for potential applicability as single-spin centers and solid-state qubits analogous to those observed in diamond and SiC. We find that isolated nitrogen vacancies meet many of the criteria for an individually addressable quantum system, but their states are close to the conduction-band edge which likely limits their utility. We therefore investigate how the properties can be tuned by complexing of the vacancy with substitutional impurities on neighboring lattice sites. Based on our comprehensive investigation, the transition-metal dopants Ti and Zr emerge as the best candidates: They preferentially substitute on the Al site and form complexes with nitrogen vacancies that possess the desired array of electronic and optical properties. Favorable charge and spin states, binding energies, and optical excitation energies are reported. Our results indicate that implantation of Ti or Zr into single-crystal AlN substrates can lead to the formation of individually addressable solid-state qubits in this material.


This work was performed in part under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and with support provided by the NSF under Grant No. DMR-143485.

The problem of detecting entanglement between a qubit and its environment is known to be complicated [1]. To simplify the issue, we study the class of Hamiltonians that describe a qubit interacting with its environment in such a way that the resulting evolution of the qubit alone is of pure dephasing type. Although this leads to some loss of generality, the pure dephasing Hamiltonian describes the dominant decohering mechanism for many types of qubits and is of fairly wide applicability. We define this situation by the requirement that the Hamiltonian of the qubit commutes with the qubit-environment interaction term. This relation means that the eigenstates of the qubit Hamiltonian form a preferred basis - they are pointer states [2,3] - selected by the form of the qubit-environment coupling. When both the qubit and the environment can initially be described by a (separable) wavefuntion (their state is pure throughout the evolution), an interaction between them that leads to a pure dephasing of the qubit always leads to the creation of entanglement between the two [4]. It is often assumed that a dephasing mechanism of this type must induce entanglement between the qubit and environment also when the environment is initially in a mixed state. We show that while the creation of qubit-environment entanglement in the pure dephasing case is possible when the environment is initially in a mixed state, the occurrence of this entanglement is by no means guaranteed.

We find that there are three types of situations (specified by the initial state of the environment and a relevant evolution operator which is derived from the Hamiltonian) when qubit-environment entanglement will not be generated. These are, the case when the initial density matrix of the environment is proportional to unity, the case when the relevant evolution operator cannot change the occupation of any of the eigenstates of the density matrix, and a non-trivial mixture of the two cases which allows dynamical evolution within closed subspaces of equal occupation.

Furthermore, we have shown that restricting the class of studied initial environmental states to a certain class of states (which is very common in any realistic qubit-environment setup) enables the use of a very powerful tool to measure the entanglement, since the state of the environment will remain static throughout the evolution (the state of the environment is found by tracing out the qubit degrees of freedom). Hence, the detection of any change of the state of the environment is then equivalent to the detection of entanglement.

B. Kraus, J. I. Cirac, S. Karnas, and M. Lewenstein, Phys. Rev. A 61, 062302 (2000).
W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).
W. H. Zurek, Phys. Rev. D 24, 1516 (1981)
R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).

About 500 color centers mainly in natural diamonds are identified, but most of the properties are unknown and only for two centers a coherent control of the spin state is proved: the NV- and ST1. Whereas the structure and nature of ST1 is unclear at the moment because it is found only in 3 samples at all; the NV- center is well investigated and can easily produced by ion beam implantation of nitrogen. This well-known NV center shows extraordinary properties but unfortunately a large phonon coupling, thus it is improper for a large numbers of applications. Whether other centers with similar properties exist, is unknown at all.
The paper will discuss the chances to find new color centers and shows an approach for a systematically searching for color centers with interesting properties like a coherent control of the spin state.

New computational methods for scale bridging--from atomistics to mesoscale--hold great promise for accelerating materials discovery and insertion into high performance technology applications. Achieving this goal in superconducting electronics relies on the fidelity of materials models throughout cryogenic temperature range and their ability to capture the connectivities among processing, microstructure, design, and performance. An agile approach to building optimized systems of software components is key to deliver timely validated models in a fast evolving multi-disciplinary development environment. This presentation will focus on advancements in our ability to deploy agile practices using next-generation integrated materials-process-design-performance simulation practices in a superconductivity research environment. Two examples serve as opportunities to share our collaborative computational methods, materials models, and tools eco-system with a wider audience, including materials engineers from other disciplines.

First, the early stages of crack initiation between metals and dielectrics using three co-dependent disparate-methodology software platforms are compared to experimental data at cryogenic and room temperatures. Adhesions calculated using molecular-level bond strengths are input live into 3D multiscale multilevel multiphysics finite element analysis (FEA) with evolving boundary conditions determined using lumped parameter models for environmental effects. Spatio-temporal scale bridging in real time is essential to capture the nonlinear interplay between all parts of the assembly and onset of distinct behaviors that dominate different stages. New agile processes were developed to automate materials data collection, introduce coarse-grain auxiliary models for reducing complexity, account for thermal distributions, and quantify uncertainty, enabling successful design spins and rapid protyping.

Second, the evolution of hysteretic stresses in thin films used to fabricate superconducting circuits is simulated by atomistic models embedded in 3D multiscale FEA routines. The changing stress matrices are tracked through deposition, patterning, fabrication of overlying structures, packaging, test, and cryo field operation. Fail-safe stress levels are defined and confirmed using high-resolution TEM analysis. Agile practices were used to reduce runtimes from weeks to hours, while also increasing model size five-fold to deal with finer length scales for defects in porous materials. Additionally, the FEA simulations can advantageously take real experimental output as input to study the physical mechanisms at work as new data become available. Results are shown to significantly reduce cycles of learning by diagnosing potential successes and failures.

Coherence in superconducting qubits is reduced by unintended coupling to fluctuating magnetic sources. However, the microscopic origins of the magnetic noise have not been satisfactorily characterized. Building on previous computational studies [PRL 112, 017001 (2014)] of magnetic spins induced by molecules adsorbed on bare Al-terminated Al₂O₃, we present a density functional theory investigation of magnetic noise associated with other Al₂O₃ surfaces likely to be encountered in experiment. Motivated by noise models involving spin clusters on the surface, we calculate the exchange interaction between adsorbed molecules, OH groups and paramagnetic O₂, as well as the magnetic state energy splitting and anisotropy, on fully hydroxylated Al₂O₃ with and without a water over-layer. Paramagnetic O₂ has been previously identified experimentally as a likely flux noise source [ArXiv:1604.00877v1]. We use the calculated magnetic quantities to parametrize Monte Carlo models in order to characterize the spin dynamics. We also present simulated x-ray absorption and x-ray magnetic circular dichroism spectra of these systems with the aim of aiding experimental surface characterization. Prepared by LLNL under Contract DE-AC52-07NA27344.

Microfabrication-induced processing artifacts have been shown to limit the coherence times of both planar and 3D superconducting qubits. Energy loss in these devices can arise as a result of interactions with two-level system defects, which are being correlated to thin layers of lossy material and/or nano-sized particulate. To this end, we present recent results from a number of different conventional and non-conventional techniques used in locating and characterizing these sources of loss on coplanar waveguide resonators. Using these observations as a metric, a novel system for supercritical fluid-assisted cleaning of superconducting aluminum features will be discussed at length. Supercritical CO₂ can serve as an effective solvent system to assist in the delivery of various co-solvents or stripping agents to even the smallest patterned features, with minimal impact to the aluminum layer. The adoption of less-invasive forms of device processing should mitigate artifact formation, translating into substantially improved coherence times.

Typical operational temperatures for superconducting quantum circuits are in the few tens of milliKelvin and excitation powers are at the level of a few photons. Low energy excitations in constituent materials can, as such, cause charge noise in single electron transistors, flux noise in SQUIDs, the non-vanishing real part of the surface impedance of superconductors and decoherence in qubits. The microscopic sources of these low energy states can include adsorbates, defects at interfaces and, potentially, nuclear spins. In any given device all of these sources are typically present and likely interacting with each other. It is therefor useful to perform experiments that allow for a systematic study of individual noise sources in isolation. Effects arising from the vacuum-substrate and superconductor-substrate interface can be avoided by making free-standing superconducting devices while bulk effects can be isolated by choosing non-oxidizing superconducting metals, high purity single crystal foils and by controlling the fraction of zero-nuclear spin isotopes. We will report on initial results of this approach to understanding and mitigating materials sources of noise in superconducting quantum devices.
This work was supported by LLNL LDRD grants 13-erd-016 and 16-SI-004

Magnetic flux noise is a dominant source of dephasing and energy relaxation in superconducting qubits. The noise power spectral density varies with frequency as 1/f with an exponent close to 1 and spans 13 orders of magnitude. Recent work indicates that the noise is from unpaired magnetic defects on the surfaces of the superconducting devices. Here, we demonstrate that adsorbed molecular oxygen is the dominant contributor to magnetism in superconducting thin films. We show that this magnetism can be reduced by appropriate surface treatment or improvement in the sample vacuum environment. We observe a suppression of static spin susceptibility by more than an order of magnitude and a suppression of 1/f magnetic flux noise power spectral density of up to a factor of 5. These advances open the door to realization of superconducting qubits with improved quantum coherence.

Semiconductor-metal interfaces are key elements in nanostructured electronics and device architectures. This is in particular true in the field of low dimensional topological superconductivity, where low dimensional semiconductor materials with high spin orbit coupling coupled to a superconducting phase constitute some of the most promising candidates in the search for materials suitable for quantum information technology[i]. I will discuss the synthesis, structural and compositional properties hybrid semiconductor-superconductor materials grown in-situ by Molecular Beam Epitaxy[ii]. Because these materials give a hard superconducting gap proximitized in the semiconductor, they serve as excellent platform for studying Andreev bound states and Majorana bound states, which opens for new application possibilities in the field. I will present on the synthesis of various types of hybrid semi-super materials and discuss the challenges and material requirements needed for realizing and eventually manipulating topological protected quantum states.

The complexities of novel devices designed for quantum information processing demand sophisticated characterization techniques with atomic-scale spatial resolution. Two examples of high relevance are, first of all, one-dimensional semiconductor/superconductor (SE/SU) heterostructures based on nanowires [1], and second, complex three-dimensional branched nanowire networks [2]. These two configurations could play a central role as the basis for solid-state quantum information processing based on manipulations of quasiparticles that exist at the boundaries of different topologies, such as Majorana fermions [3].

A common requirement in both systems is the need to achieve the highest possible crystalline structural quality, especially at the interfaces and junctions between different materials. For instance, structural disorder in SE/SU interfaces leads to the appearance of the soft gap, inducing soft-gap states, which act as a source of decoherence of Majorana modes [4]. In the case of branched nanowire networks, high crystalline quality at junctions is required to realize Majoranas with nearly ballistic transport. In addition, the formation of defects in the nanowires and in the interfaces could lead to spurious Majoranas, which should be avoided.

These considerations provide strong motivation to perform a detailed investigation of the crystalline structure of these systems, together with the associated mechanisms for strain relaxation that arises when different materials are combined. In this respect, Transmission Electron Microscopy (TEM) provides a unique toolbox to achieve this goal. Electron Microscopy fulfils many of the requirements for the characterization of the structure and properties of nanomaterials employed in applications for quantum computation.

In this talk, we illustrate this paradigm by presenting the structural characterization using TEM of 1D InSb/Al and InSb/NbTiN (SE/SU) heterostructures based on nanowires and of InSb-nanowire complex network architectures. We study in particular the structural quality of interfaces in these SE/SU systems. In the case of the nanowire networks, we demonstrate the appearance of remarkable structural defects at the junctions, which can be an additional source of strain in the system. Our results provide crucial input to understand the electronic and transport properties in these novel systems, which ultimately allow them to be used in solid-state quantum information processing.


[1] P. Krogstrup, et. al. Nature Materials 14, 400 (2015)
[2] S. R. Plissard, et. al. Nature Nanotechnology 8, 859 (2013)
[3] Mourik, V. et al. Science 336, 1003 (2012)
[4] S. Takei, et. al. Phys. Rev. Lett. 110, 186803 (2013)

Heterostructures of InAs, AlSb and GaSb are of particular interest in the field of topological quantum information processing. Strong spin-orbit coupling in low dimensional InAs and its ability to form transparent contacts to superconductors make it suitable for realizing topological superconductivity in semiconductor-superconductor heterostructures^1–4. For their utilization in quantum information processing, low dimensional systems require sufficiently low levels of disorder⁵. This work presents evidence of the sources of disorder in the two dimensional energy landscapes of high mobility InAs/AlSb quantum wells wherein gated low temperature electron mobility exceeding 750,000 cm²/Vs has been achieved. In heterostructures in which subbands within an InAs channel quantum mechanically couple to those in a GaSb channel a two-dimensional topological insulator is predicted to exist⁶. The effects of disorder are considered in interpreting low temperature transport experiments on high quality InAs/GaSb bilayers gate-tuned between the predicted topological insulator and normal insulator regimes.
¹ J.D. Sau, R.M. Lutchyn, S. Tewari, and S. Das Sarma, Phys. Rev. Lett. 104, 040502 (2010).
² J. Alicea, Phys. Rev. B 81, 125318 (2010).
³ R.M. Lutchyn, J.D. Sau, and S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010).
⁴ Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010).
⁵ J.D. Sau, S. Tewari, and S. Das Sarma, Phys. Rev. B 85, 064512 (2012).
⁶ C. Liu, T.L. Hughes, X.L. Qi, K. Wang, and S.C. Zhang, Phys. Rev. Lett. 100, 236601 (2008).

Trapped ions are sensitive to electric-field noise from trap-electrode surfaces. This noise has been an obstacle to progress in trapped-ion quantum information processing experiments for more than a decade. It causes motional heating of the ions, and thus quantum-state decoherence. This heating is anomalous because it is not easily explained by typical technical-noise sources. Experimental evidence of its dependence on ion-electrode distance, frequency, and electrode temperature points to the surface, rather than the bulk, of the trap electrodes as the origin. In this presentation, I will review experimental efforts and theoretical models to help identify and reduce or eliminate the root source of the anomalous heating.

Because of their prospects for miniaturization and scalability, trapped ions represent a promising implementation of qubits for quantum computers. However, their widespread adoption into quantum computing architectures has been severely hindered by the effect of anomalous heating, an observed phenomenon of ion heating rates orders of magnitude higher than the Johnson noise limit. As the ion-electrode distance is reduced, the heating rate grows precipitously, resulting in a substantial decrease in the available time for practical gate operations to be performed. Despite a number of recent experiments aimed at better characterizing this phenomenon, the microscopic sources of anomalous heating are still not well understood. In this work, we perform quantitative calculations of the heating rates produced by a wide range of surface-adsorbate combinations by parametrizing a patch potential model with potentials and dipole moments that come directly from density functional theory simulations employing highly accurate dispersion-corrected hybrid exchange-correlation functionals. Our results provide a framework for predicting which surface-adsorbate combinations will yield the smallest heating rates based upon adsorbate masses, binding strengths, and potential widths. One of the key finding of these calculations is that a variety of hydrocarbon fragments show a substantial increase in their heating rates at temperatures similar to those at which recent experiments have observed a rapid onset of heating, thus suggesting that hydrocarbons may be responsible for these experimental signatures. In combination with recent studies on the effects of surface roughening, this work helps to provide a detailed picture of some of the key materials sources of heating in ion traps.Prepared by LLNL under Contract DE-AC52-07NA27344.

Advanced fabrication techniques focusing on eliminating lossy dielectrics and meticulously cleaning interfaces have enabled increased quantum coherence in superconducting quantum bits (qubits). However, in order to architect a large system of interconnected qubits, dense control lines must be routed in 3D while preserving qubit coherence. We report on our development of superconducting-indium-bump flip-chip technology for connecting a multi-layer signal routing carrier chip to a pristine qubit chip. We will report on process development for integrating indium into our qubit fabrication as well as the performance of this superconducting link from DC to microwave frequencies.

Molecular Beam Epitaxy (MBE) grown aluminum is valuable for circuit elements in superconducting qubits because of its low microwave loss which is important in circuit quantum electrodynamic architectures such as transmon qubits. Thin Al films are also used to make Josephson junctions where interfacial roughness leads to inhomogeneity of the tunnel current across the barrier. The presented observations are also important from a fundamental materials perspective in that Al growth on Si has been used as a model system to investigate nucleation and growth physics.
In this paper, the nucleation and growth of Al on 7x7 and √3X√3 R30 Al reconstructed Si (111) surface is compared using atomic force microscopy (AFM). Strain-free Al is grown with an atomically abrupt metamorphic interface using MBE. The reconstructed surfaces are verified using Reflection High Energy Electron Diffraction prior to growth. These surfaces are selected because they are both clean and shown to influence the formation of twins in Al. The evolution of Al nucleation and mound formation is obtained from two samples using non-rotating substrates leading to non-uniform growth across the substrate. The morphology of Al for different amounts of coverage are characterized using AFM at different locations across the wafer.
The growth of Al on both the 7x7 and √3X√3 surfaces exhibit 3D island growth, but the evolution of growth is dramatically different. On the 7x7 Si surface, Al grows in small islands approximately 18 nm in diameter. Islands form uniformly across the substrate, and growth appears to proceed uniformly. Alternatively, on the √3X√3 Si surface, Al atoms exhibit clear preference to form islands near the step edges that are approximately 26 nm in diameter. During Al growth, islands increase in size and number, expanding out from step edges until they cover the whole substrate. Despite these nucleation differences, both aluminum films continue to grow in a 3D manner with rms roughnesses that are less than 0.5 nm for 100-nm thick films.

Superconducting quantum circuits incorporating Josephson junctions (JJs) show great promise as qubits for the realization of quantum computing. Calculations have shown that dissipative two-level systems resulting from interstitial hydrogen impurities in Al₂O₃ could contribute to losses in superconducting circuits depending on the specific O-O bonds lengths. Characterization of the fabricated interfaces at the atomic scale provides the fundamental understanding of not only how the material was grown, but how bonding and vacancies at the interfaces could affect dielectric losses. In this work we study the interface between epitaxial Al and c-plane Al₂O₃ grown by molecular beam epitaxy. By using a combination of focused ion beam and mechanical polishing, the interface is prepared in three perpendicular orientations. Aberration-corrected scanning transmission electron microscopy (STEM) is used to probe the local atomic structure and bonding at the interface. By imaging in three orientations, an understanding of the distances and geometries of the interfacial misfit dislocations is obtained. The experimental observations are validated by molecular dynamics simulations, density functional theory calculations, and STEM image simulations.

High-purity superconductors that have exceedingly low microwave loss are of critical importance to qubit devices made using circuit quantum electrodynamic architectures. Single crystal aluminum is one of the leading materials for this purpose. Recent results show that this has been implemented through metamorphic epitaxial aluminum growth via molecular beam epitaxy on silicon. Understanding the superconductor-substrate interfaces and the bonding defects at the interfaces is important from the perspective of the fundamental microwave loss mechanisms and possible formation of two-level system defects. In this study, molecular dynamics (MD) simulations of Al(111)/Si(111) interfaces have been carried out employing an angular embedded atom method potential capable of describing interactions between Si and Al, to account for both covalent and metallic bonds. The Frank-Bilby theory is used to analyze the interfacial misfit dislocation contents at the MD simulation obtained interfaces. The findings from the atomistic modeling and theoretical analysis are then discussed. Experimental validation of models from atomic resolution scanning transmission electron microscopy clearly show primary misfit dislocations for the majority of the strain relief, and evidence of a secondary structure allowing for complete relaxation of the Al-Si misfit strain.

Al/AlO_x/Al Josephson junctions are key elements in superconducting quantum bits (qubits) that hold great promise for the realization of quantum computing and quantum information processing. However, the implementation of quantum computing based on Josephson junctions is limited by decoherence in the qubits. The decoherence is believed to be directly correlated with certain microstructural features of the materials in Josephson junctions of the qubits. Many transport properties measurements and theoretical modeling studies have been carried out to figure out the relationship between the microscopic structure of Josephson junctions and the origin of decoherence. Those investigations have greatly advanced our understanding of the origin of decoherence from materials microstructure perspective, but there have been very few direct experimental studies on the microstructure of Al/AlO_x/Al Josephson junctions at nanometer and atomic scale.

Here, we studied the microscopic structure of Al/AlOx/Al junctions using transmission electron microscopy (TEM). With the capabilities of atomic resolution imaging, diffraction and electron energy loss spectroscopy (EELS) provided by TEM, we investigated different aspects of the microstructure of Al/AlO_x/Al Josephson junction. We have shown a nanoscale intermixing of different elements (Al, O and Si) at the interface [1,2]. The atomic structure at Al/AlO_x interfaces in the junctions was directly measured by atomic resolution imaging and a distortion of the Al atomic lattices at the interfaces was found. High resolution imaging was also used to directly measure the thickness distribution of the AlO_x tunnel barriers. The results show that only a small portion of the tunnel barrier contributes to the tunneling of electrons in those junctions [3]. The atomic structure of the amorphous tunnel barrier was revealed by nano beam electron diffraction, atomic resolution imaging and EELS. It was found that there is oxygen deficiency at the Al/AlO_x interfaces in the junctions, while the interior of the barrier shows similar atomic structure as the bulk phase of amorphous Al₂O₃ [4].

The detailed results on the structure at various interfaces in the junctions may help understanding the role of interface states that contribute to decoherence in quibits. The information on the atomic structure of the tunnel barrier is critical for finding out the origin of two-level fluctuators in the amorphous oxide barrier and their contribution to decoherence in Josephson junction based qubits.

[1] L. J. Zeng, P. Krantz, S. Nik, P. Delsing, and E. Olsson, J. Appl. Phys. 117, 163915 (2015)
[2] L. J. Zeng, T. Greibe, S. Nik, C. M. Wilson, P. Delsing, and E. Olsson, J. Appl. Phys. 113, 143905 (2013)
[3] L. J. Zeng, S. Nik, T. Greibe, P. Krantz, W. C. Wilson, P. Delsing, and E. Olsson, J. Phys. D: Appl. Phys. 48, 395308 (2015)
[4] L. J. Zeng, D. T. Tran, C-W Tai, G. Svensson, and E. Olsson, submitted (2016)

The realization of devices for quantum information technology is a major goal in information science. Among the different technology platforms, superconducting circuits are perhaps the most promising approach. The basic units, quantum bits (qubits), consist of several Josephson junctions (JJs), which are typically fabricated on the basis of Al/AlO_x/Al-layer systems. Much progress has been achieved with respect to coherence times which have increased by five orders of magnitude in the past 15 years [1]. However, further improvement of the coherence times is necessary. A major source of decoherence appear to be two-level tunneling systems (TLS) [2], which have been associated with structural anomalies of the disordered AlO_x-tunnel barrier [3]. In recent experiments, the coupling to strain and electric fields of individual TLS in JJs could be studied in detail [4,5], whereas a global determination of TLS densities can be derived from measurements of the low-temperature dielectric properties of the AlO_x-films [6]. However, the identification of the microscopic nature of the TLSs was not possible up to now and prevents the deterministic reduction of the TLS density. Analytical transmission electron microscopy (TEM) yields structural and chemical properties on an atomic scale and recent work has shown the potential of these techniques for analyzing and improving the properties of JJs and qubits [7,8].
In this work we study differently prepared Al/AlO_x/Al-layer systems with AlO_x-layers which were fabricated under well-controlled oxidation conditions. We specifically aim to understand whether the TLS density can be reduced by optimizing the structural and chemical properties of the AlO_x-tunnel barrier. For this purpose, we correlate structural and chemical properties obtained by analytical TEM with data on the TLS density from low-temperature measurements of capacitors with AlO_x-films as dielectric.
TEM shows that grain boundaries in the lower Al-electrode induce significant thickness variations of the AlO_x tunnel barrier which will lead to a spatially inhomogeneous tunnel current. Nanocrystalline regions are found in the AlO_x-layer. Analyses of the chemical composition demonstrate that the oxygen concentration in AlO_x is strongly influenced by the oxidation conditions (AlO_0.5 for standard oxidation conditions and AlO_1.1 for UV-enhanced conditions). Changes of the oxidation conditions lead to significant changes of the TLS density.

[1] M. H. Devoret, R. J. Schoelkopf, Science 339, 1169 (2013)
[2] J.M. Martinis et al., Phys. Rev. Lett. 95, 210503 (2005)
[3] T.C. DuBois, S.P. Russo, J.H. Cole, New J. Phys. 17, 023017 (2015)
[4] G.J. Grabovskij et al., Science 338, 232 (2012)
[5] J. Lisenfeld et al., Scientific Rep. 6, 23786 (2016)
[6] W.A. Phillips Rep. Prog. Phys. 50, 1657 (1987)
[7] V. V. Roddatis et al., J. Appl. Phys. 110, 123903 (2011)
[8] L. J. Zeng et al., J. Phys. D: Appl. Phys. 48, 395308 (2015)

Josephson junctions are an essential element of superconducting quantum circuits, providing a non-linear, non-dissipative inductance. Common fabrication techniques of overlap junctions using double-angle evaporation result in a range of parameters, as evidenced by variations in critical current for nominally identical junctions. The corresponding spread in qubit frequencies has implications for scaling quantum processors to larger systems. We assess our junction variability and discuss potential mitigation schemes.

One of the major limitations to constructing densely-integrated cryogenic electronic systems is the electrical interconnect technology. Dense, controlled-impedance, superconducting cables with small cross-sections are desirable, especially for quantum computing applications. Building superconducting flexible cables using an embedded structure is attractive since it has been observed to increase reliability and is necessary for cables in configurations with reduced cross-talk, such as stripline. However, material selection, fabrication limitations and cable performance are issues that must be considered. In this paper, we explore fabrication and performance trade-offs related to narrow Nb superconductor lines embedded in polyimide. A low loss polymer dielectric (polyimide PI-2611) was chosen for the encapsulation layer as well as the cable substrate. A low temperature polyimide cure process was developed in order to protect the Nb superconductivity during subsequent fabrication processes. We found that embedded Nb superconducting cable shows very small transmission line loss and enhanced mechanical reliability. More importantly, this type of embedded structure can potentially be applied to build more complex cables, such as stripline or multi-conductor cable.
In this presentation, we will present details of the fabrication and characterization of embedded Nb superconducting flexible structures. Comparison of materials characterization results of Nb thin film on PI-2611 substrate and in PI-2611 encapsulation layer will be shown. Embedded Nb DC cables and half-wavelength, capacitively-coupled embedded Nb microstrip resonators constructed on 20 um-thick PI-2611 substrates with 0.25 um-thick Nb metallization have been fabricated and studied. We will report on experimental results of DC and RF testing, as well as mechanical reliability testing of non-embedded and embedded structures. In DC testing, critical temperature (T_c) and critical current (I_c) of embedded DC cables with line width of ~ 50 um were measured. In RF testing, loaded quality factor (Q_L) of embedded resonators have been measured in a temperature range of ~ 1.2 K – 4.2 K and in 2-20 GHz frequency range. For comparison, corresponding results of non-embedded structures will also be presented. Furthermore, significant improvements in reliability were observed (i.e., less degradation in I_c) for embedded DC cables. For example, after 500 room-temperature tension-compression bending cycles, the I_c degradation of embedded DC cables is less than 10 % while that of non-embedded DC cables is more than 26 %. These are promising results that provide guidance on materials choices and fabrication processes that are useful for construction of flexible, dense and low signal loss electrical interconnect for cryogenic electronics applications.

Diamond has a number of extreme properties that lend themselves readily to applications in quantum information processing and metrology. For example, defects in diamond such as silicon / nitrogen – vacancy complexes exhibit room temperature single photon emission and the ultra high resonant frequencies achievable in diamond Nano-Electro-Mechanical Systems (NEMS) allow them to be cooled into the ground state at temperatures achievable with a dilution refrigerator.

In the case of single photon centres, a key issue is control over position. There are various approaches to this, one of the most promising being to make nanoparticles of diamond containing the required colour centre and position them manually. To this end, diamond films containing SiV or NV centres have been milled to nanoscale particles and stable aqueous colloids produced. This work will detail the production and purification of such particles.

For NEMS the main issue is detection of motion for which is exploitation of superconductivity is proposed. Superconductivity QUantum Interference Devices (SQUIDs) are highly sensitive to magnetic flux. This effect can be exploited to detect the motion of a cantilever embedded in a SQUID loop, as its deflection will modulate the area and hence flux through the loop. This work will demonstrate the fabrication of diamond NEMS and SQUIDs towards this device.

Mid-IR chemical imaging of tissues and cells is a powerful research tool, as rotational and vibrational spectra of large biological molecules lies in this part of spectra. Currently cell micro-spectroscopy in Mid-IR required using synchrotron as a light source. Development of quantum-cascade semiconductor lasers and demonstration of detection and even direct energy measurement of single Mid-IR photons suggests new perspectives in this field.
Main obstacle to use single-photon techniques in Mid-IR for living cell research was considered to be background of room temperature thermal radiation, which would overload photon detector. It is possible to overcome this difficulty by working with frozen cell inside cryogenic enclosure and with using cold spectrometer. Freezing is routinely used for cell storage, and IR spectroscopy at low intensities will be absolutely non-distractive. More intriguing possibility is to place inside cryogenic enclosure a thin, Mid-IR transparent microfluidic device with living cells at room temperature. This way thermal radiation background can be significantly suppressed and IR luminescence can be detected with cooled spectrophotometer at a single-photon level. In addition to measurements of absorption and reflection spectra and using different techniques to excite photo-luminescence, one should be able to look for chemo-luminescence produced due to cell metabolic processes. Thus, we can look at processes incide living cell using new techniques, which will be absolutely non-destructive and do not required introduction of foreign molecules or nano-particles into living cells.
This work was supported by LLNL LDRD grants 13-ERD-016 and 16-SI-004.

GaN is an important wide band gap material that is widely used in an optoelectronics, high-power electronics and photonics[1]. Its high refractive index of 2.39(λ= 600 nm) and manufacturable property enable low-loss cavities and photonic integrated circuits.[2] GaN quantum dots have been demonstrated as a quantum light source, typically at short wavelength (>4eV).[3] Although theoretical studies of defects in GaN have been reported,[4] single defect emission from GaN has not been reported.
Here, we report on room-temperature, photostable and bright single photon emitters in GaN grown on sapphire substrate with a photoluminescence in the visible spectrum. These studies use GaN with a thickness of 2 μm grown by MOCVD. The single photon emitters in GaN are studied at room-temperature and low temperature (3.5 K) using a confocal microscope setup with a 532 nm excitation laser. The emitters have strong and narrow (<5nm), linearly polarized single photon fluorescence in the 615-780 nm spectral band at room temperature. The excited state lifetime is 2 ns. Low temperature measurements indicate a narrow zero phonon line with line width of 0.6 nm, and excited state.
This single photon emitter in GaN is a promising candidate for on-chip quantum information processing.
Reference
[1] T. J. Flack, B. N. Pushpakaran, and S. B. Bayne, GaN Technology for Power Electronic Applications: A Review, J. of Elec. Mater., 45, 2673 (2016).
[2] N. V. Triviño, R. Butté, J. Carlin, and N. Grandjean, Continuous Wave Blue Lasing in III-Nitride Nanobeam Cavity on Silicon, Nano Lett., 15, 1259 (2015).
[3] M. J. Holmes, K. Choi, S. Kako, M. Arita, and Y. Arakawa, Room-Temperature Triggered Single Photon Emission from a III-Nitride Site-Controlled Nanowire Quantum Dot, Nano Lett., 14, 982 (2014).
[4] X. Wang, M. Zhao, Z. Wang, X. He, Y. Xi, and S. Yan, Spin-polarization of V_GaO_N center in GaN and its application in spin qubit, Appl. Phys. Lett., 100, 192401 (2012).