Relativistic effects in complex compounds containing heavy elements: ternary Cu-Tl-X (X = S/Se/Te).

Cu-chalcogenides are a large group of multifunctional compounds traditionally used in photovoltaics and optoelectronics. Their bandgap sizes usually decrease with the element masses, e.g., 2.68, 1.68, and 1.04 eV for CuAlSe2, CuGaSe2, and CuInSe2, respectively. Cu-Tl-X (X = S/Se/Te) with even heavier thallium (Tl) has received recent attention in topological insulators and high-performance thermoelectric converters. While the novel applications may be related to Tl relativistic effects, first-principles investigations are scarce for these complex compounds. Here, we reveal the relativistic effects in Cu-Tl-X using a tailored density-functional-theory approach. Three relativistic terms of mass-velocity, Darwin, and spin-orbit-coupling play distinct roles. In diamond-like CuTlX2, the mass-velocity correction reduces the conduction band position and contributes to minimizing the bandgaps. The relativistic bandgap of CuTlS2 of 0.11 eV is substantially smaller than 1.7 eV without considering the relativistic effects. In CuTlTe2, the spin-orbit-coupling splits the valence bands, resulting in an exotic band inversion. CuTlSe2 lies on the boundary of normal and inverted band topologies. Interestingly, the relativistic core contraction is so strong that it may favor non-centrosymmetric defective structures with stereoactive lone-pair electrons. The bandgap of the defective structure is much larger, leaving the system little chance to develop an inverted band topology. Our work provides deep insights into understanding the relativistic band topologies of the complex Cu-Tl-X compounds.

Converting a Monolayered NbSe2 into an Ising Superconductor with Nontrivial Band Topology via Physical or Chemical Pressuring.

Two-dimensional transition metal dichalcogenides possessing superconductivity and strong spin-orbit coupling exhibit high in-plane upper critical fields due to Ising pairing. Yet to date, whether such systems can become topological Ising superconductors remains to be materialized. Here we show that monolayered NbSe2 can be converted into Ising superconductors with nontrivial band topology via physical or chemical pressuring. Using first-principles calculations, we first demonstrate that a hydrostatic pressure higher than 2.5 GPa can induce a p-d band inversion, rendering nontrivial band topology to NbSe2. We then illustrate that Te-doping can function as chemical pressuring in inducing nontrivial topology in NbSe2-xTex with x ≥ 0.8, due to a larger atomic radius and stronger spin-orbit coupling of Te. We also evaluate the upper critical fields within both approaches, confirming the enhanced Ising superconductivity nature, as experimentally observed. Our findings may prove to be instrumental in material realization of topological Ising superconductivity in two-dimensional systems.

Coexistence of Robust Edge States and Superconductivity in Few-Layer Stanene.

High-quality stanene films have been actively pursued for realizing not only quantum spin Hall edge states without backscattering, but also intrinsic superconductivity, two central ingredients that may further endow the systems to host topological superconductivity. Yet to date, convincing evidence of topological edge states in stanene remains to be seen, let alone the coexistence of these two ingredients, owing to the bottleneck of growing high-quality stanene films. Here we fabricate one- to five-layer stanene films on the Bi(111) substrate and observe the robust edge states using scanning tunneling microscopy/spectroscopy. We also measure distinct superconducting gaps on different-layered stanene films. Our first-principles calculations further show that hydrogen passivation plays a decisive role as a surfactant in improving the quality of the stanene films, while the Bi substrate endows the films with nontrivial topology. The coexistence of nontrivial topology and intrinsic superconductivity renders the system a promising candidate to become the simplest topological superconductor based on a single-element system.

Kinetic pathways towards mass production of single crystalline stanene on topological insulator substrates.

As a highly appealing new member of the two-dimensional (2D) materials family, stanene was first epitaxially grown on a three-dimensional topological insulator of Bi2Te3; yet, to date, a standing challenge is to drastically improve the overall quality of such stanene overlayers for a wide range of potential applications in next-generation quantum devices. Here we use state-of-the-art first-principles approaches to explore the atomistic growth mechanisms of stanene on different Bi2Te3(111)-based substrates, with intriguing discoveries. We first show that, when grown on experimentally studied Te-terminated Bi2Te3, stanene would follow an unusual partial-layer-by-partial-layer growth mode, characterized by short-range repulsive pairwise interactions of the Sn adatoms; the resultant stanene overlayer is destined to contain undesirable grain boundaries. More importantly, we find that stanene growth on Bi2Te3(111) pre-covered with a Bi bilayer follows a highly desirable nucleation-and-growth mechanism, strongly favoring single crystalline stanene. We further show that both systems exhibit pronounced Rashba spin-orbit couplings, while the latter system also provides new opportunities for the potential realization of topological superconductivity in 2D heterostructures. The novel kinetic pathways revealed here will be instrumental in achieving the mass production of high-quality stanene with emergent physical properties of technological significance.