Dominik Gresch

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides X P 2 ( X = Mo , W)

The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe the prediction of a type-II Weyl semimetal phase in the transition metal diphosphides MoP_{2} and WP_{2}. These materials are characterized by relatively simple band structures with four pairs of type-II Weyl points. Neighboring Weyl points have the same chirality, which makes the predicted topological phase robust with respect to small perturbations of the crystalline lattice. In addition, this peculiar arrangement of the Weyl points results in long topological Fermi arcs, thus making them readily accessible in angle-resolved photoemission spectroscopy.

Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging, problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous k . p models, tight-binding models, and ab initio calculations. We apply the method to compute and identify Chern, Z(2), and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with nontrivial topologies. We expect that our work will allow researchers to (a) identify topological materials optimal for experimental probes, (b) classify existing compounds, and (c) reveal materials that host novel, not yet described, topological states.

Hidden Weyl Points in Centrosymmetric Paramagnetic Metals

The transition metal dipnictides TaAs2 , TaSb2 , NbAs2 and NbSb2 have recently sparked interest for exhibiting giant magnetoresistance. While the exact nature of magnetoresistance in these materials is still under active investigation, there are experimental results indicating anisotropic negative magnetoresistance. We study the effect of magnetic field on the band structure topology of these materials by applying a Zeeman splitting. In the absence of magnetic field, we find that the materials are weak topological insulators, which is in agreement with previous studies. When the magnetic field is applied, we find that type-II Weyl points form. This result is found first from a symmetry argument, and then numerically for a k.p model of TaAs2 and a tight-binding model of NbSb2. This effect can be of help in search for an explanation of the anomalous magnetoresistance in these materials.

Optimizing spin-orbit splittings in InSb Majorana nanowires

Semiconductor-superconductor heterostructures represent a promising platform for the detection of Majorana zero modes and subsequently the processing of quantum information using their exotic non-Abelian statistics. Theoretical modeling of such low-dimensional semiconductors is generally based on phenomenological effective models. However, a more microscopic understanding of their band structure and, especially, of the spin-orbit coupling of electrons in these devices is important for optimizing their parameters for applications in quantum computing. In this paper, we approach this problem by first obtaining a highly accurate effective tight-binding model from ab initio calculations in the bulk. This model is symmetrized and correctly reproduces both the band structure and the wavefunction character. It is then used to determine Dresselhaus and Rashba spin-orbit splittings induced by finite size effects and external electric field in zincblende InSb one- and two-dimensional nanostructures as a function of growth parameters. The method presented here enables reliable simulations of realistic devices, including those used to realize exotic topological states.

Calculating Topological Invariants with Z2Pack

The topological phase of non-interacting electronic bandstructure can be classified by calculating integer invariants. In this chapter, we introduce the Chern invariant that classifies 2D materials in the absence of symmetry. We then show that this invariant can be used as the building block for the classification of topological insulators, semimetals, and symmetry-protected topological phases. We show how this classification is performed in practice by introducing Z2Pack, a tool which allows calculating topological invariants from \({\mathbf {k}}\cdot \mathbf {p}\) and tight-binding models, as well as first-principles calculations.

Topological classification with Z2Pack(Conference Presentation)

We present a general technique for capturing various non-trivial topologies in the band structure of materials, which often arise from spin-orbit coupling. The technique is aimed at insulators and semimetals. Of insulators, Chern, Z2, and crystalline topological insulators can be identified. Of semimetals, the technique captures non-trivial topologies associated with the presence of Weyl and Dirac points in the spectrum. A public software package -- Z2Pack -- based on this technique will be presented. Z2Pack is an easy-to-use, well documented Python package that computes topological invariants and illustrates non-trivial features of Berry curvature. It works as a post-processing tool with all major first-principles codes, as well as with tight-binding models. As such, it can be used to investigate materials with strong spin-orbit coupling.