Structural Goldilocks Effect in The Ultra-Pure Topological Semimetal PtSn₄

The Residual Resistivity Ratio (RRR) serves as a pivotal metric to gauge sample quality for metals, where RRR is the ratio of the resistivity at room temperature (~ 300 K) to the resistivity at base temperature (~ 0 K). For common metals like Au or Cu, transport behavior at 0 K primarily reflects the inherent defects and disorders within the material. Whereas at room temperature, the electronic transport is substantially influenced by other factors, such as phonons. Therefore, a sample with a high RRR can be valued as possessing fewer intrinsic defects and less disorder. However, such pristine materials are tough to come by and often require a lot of effort to optimize the crystal growth technique to make defect-free samples.<br/><br/>PtSn₄is a rare exception, and shows ultra-low resistivity around 2 K and remarkable RRR values exceeding 1000. One of the other dominating electronic properties of this material is its ultrahigh magnetoresistance (XMR), which onsets at 30 K. Magnetoresistance (MR) is the resistance that develops in a material as a response to the application of the magnetic field. PtSn₄ is also classified as a novel topological semimetal and hosts Dirac arcs in its momentum space such that the conduction and valence band touch in loops and not at a point or line. Previous studies have linked this high mobility and XMR in PtSn₄ to its distinctive Fermi surface and the band dispersion of nodal arc surface states. Yet, despite numerous reports suggesting a connection between these surface states and electronic transport properties, a clear physical relationship remains elusive. Therefore, it is crucial to understand the origin of the high mobility and XMR in PtSn₄, which will also shed light on the underlying relation between the non-trivial band topology and experimentally observed electrical transport properties in PtSn₄.<br/><br/>Through this work on PtSn₄, we aim to resolve the question about the origin of the high carrier mobility by perturbing the system using defects and chemical substitution. This approach allows to disentangle whether the high mobility in PtSn₄ originates from forbidden backscattering, which results from topologically protected surface states, or whether it is related to an unusually low defect density. Using electrical transport measurements, scanning tunneling microscopy (STM) and density functional theory (DFT) calculation we confirm that PtSn₄ is remarkably robust against chemical substitution and resistant to defect introduction into its lattice. Comparing it with AuSn₄ and IrSn₄, which form locally similar structures to PtSn₄, we find significantly lower RRR values in the latter two. This highlights the uniqueness of the PtSn₄ structure. The high electron mobilities in PtSn₄ can be attributed to the defect-intolerant Pt layers, which dominate electronic transport. Our STM mappings quantitatively assess the defect concentration in PtSn₄, revealing surprisingly low defects in the Pt layers compared to higher concentrations in the Sn layers. DFT calculations corroborate these findings, showing higher defect formation energies for Sn within the PtSn₄ lattice and the favorable energy associated with introducing defects into the AuSn₄structure. Thus, we conclude that the crystal chemistry in PtSn₄ is a good example of a structural Goldilocks effect where the naturally defect-intolerant layers support the long electron-free paths.