We consider the problem of calculating weak and strong topological indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized one dimension. Although this is not smoothly defined on two-torus, it respects T symmetry system allows for definition Z_2 terms polarization. 3D apply approach T-invariant planes. illustrate method with first-principles calculations GeTe HgTe under [001] [111]...

We consider the problem of constructing Wannier functions for Z_2 topological insulators in two dimensions. It is well known that there a obstruction to construction Chern insulators, but it has been unclear whether this also true case. Kane-Mele tight-binding model, which exhibits both normal (Z_2-even) and (Z_2-odd) phases as function model parameters. In Z_2-even phase, usual projection-based scheme can be used build representation. Z_2-odd we do find obstruction, only if one insists on...

Based on the ab initio calculations, we show that MoTe_{2}, in its low-temperature orthorhombic structure characterized by an x-ray diffraction study at 100 K, realizes 4 type-II Weyl points between Nth and (N+1)th bands, where N is total number of valence electrons per unit cell. Other WPs nodal lines different other bands also appear close to Fermi level due a complex topological band structure. We predict series strain-driven phase transitions this compound, opening wide range possible...

The intense theoretical and experimental interest in topological insulators semimetals has established band structure topology as a fundamental material property. Consequently, identifying topologies become an important, but often challenging problem, with no exhaustive solution at the present time. In this work we compile series of techniques, some previously known, that allow for to problem large set possible topologies. method is based on tracking hybrid Wannier charge centers computed...

Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by structure topology. While some metals these are direct analogues of elementary particles relativistic quantum field theory, other can have symmetries that give rise to quasiparticles, fundamentally different from those known high-energy physics. Here we report on a new type topological -- triple point fermions realized with symmorphic crystal structure, which host...

We report a combined experimental and theoretical study of the candidate type-II Weyl semimetal MoTe2. Using laser-based angle-resolved photoemission we resolve multiple distinct Fermi arcs on inequivalent top bottom (001) surfaces. All surface states observed experimentally are reproduced by an electronic structure calculation for crystal that predicts topological state with 8 points. further use systematic calculations simulating different point arrangements to discuss robustness...

We report angle-resolved photoemission experiments resolving the distinct electronic structure of inequivalent top and bottom (001) surfaces WTe2. On both surfaces, we identify a surface state that forms large Fermi-arc emerging out bulk electron pocket. Using calculations, show these Fermi arcs are topologically trivial their existence is independent presence type-II Weyl points in band structure. This implies observation alone does not allow identification WTe2 as topological semimetal....

The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II semimetals that host such are predicted to exhibit a new type of chiral anomaly possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe prediction semimetal phase in transition metal diphosphides MoP2 WP2. These materials characterized by relatively simple band structures with four pairs points. Neighboring have same chirality,...

Recently published discoveries of acoustic and optical mode inversion in the phonon spectrum certain metals became first realistic example non-interacting topological bosonic excitations existing materials. However, observable physical technological use such phases remained unclear. In this work we provide a strong theoretical numerical evidence that for class metallic compounds (known as triple point metals), points spectrum, at which three (two one acoustic) modes (bands) cross, represent...

Superconductor proximitized one-dimensional semiconductor nanowires with strong spin-orbit interaction (SOI) are at this time the most promising candidates for realization of topological quantum information processing. In current experiments SOI originates predominantly from extrinsic fields, induced by finite size effects and applied gate voltages. The dependence transition in these devices on microscopic details makes scaling to a large number difficult unless material dominant intrinsic...

Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space metals with space-time inversion ($\mathcal{PT}$) symmetry and weak spinorbit coupling. We show these are quaternion charges, similar to those describing disclinations in biaxial nematics. Starting from two-band considerations, develop complete many-band description presence...

We develop a unified numerical approach for modeling semiconductor-superconductor heterostructures. All the key physical ingredients of these systems---orbital effect magnetic field, superconducting proximity effect, and electrostatic environment---are taken into account on equal footing in realistic device geometry. As model system, we consider indium arsenide (InAs) nanowires with an epitaxial aluminum (Al) shell, which is one most promising platforms Majorana zero modes. demonstrate...

The interplay between electronic correlations and topological protection may offer a rich avenue for discovering emergent quantum phenomena in condensed matter. However, have so far been little investigated Weyl semimetals (WSMs) by experiments. Here, we report combined optical spectroscopy theoretical calculation study on the strength of kagome magnet Co3Sn2S2 influence its WSM state expected within single-particle picture. kinetic energy estimated from our data is about half that obtained...

We develop a technique for constructing Bloch-like functions 2D ${\mathbb{Z}}_{2}$ insulators (i.e., quantum spin-Hall insulators) that are smooth of $\mathbf{k}$ on the entire Brillouin-zone torus. As initial step, occupied subspace insulator is decomposed into direct sum two ``Chern bands,'' is, topologically nontrivial subspaces with opposite Chern numbers. This decomposition remains robust independent underlying symmetries or specific model features. Starting bands obtained in this way,...

We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization topological charge pumping quantum Hall systems to cold atoms lattices. Time-of-flight measurement along one spatial direction combined with situ detection transverse provides direct measure system's Chern number, as we illustrate by calculations Hofstadter lattice. Based analogy Wannier function techniques theory, method is very general and also allows...

Recent experiments on Majorana fermions in semiconductor nanowires [S. M. Albrecht, A. P. Higginbotham, Madsen, F. Kuemmeth, T. S. Jespersen, J. Nyg\aa{}rd, Krogstrup, and C. Marcus, Nature (London) 531, 206 (2016)] revealed a surprisingly large electronic Land\'e $g$ factor, several times larger than the bulk value---contrary to expectation that confinement reduces factor. Here we assess role of orbital contributions electron factor quantum dots. We show an...

We study the transition of $\ensuremath{\nu}=1/3$ and $2/5$ fractional quantum Hall states honeycomb Hofstadter model as we tune to a two-orbital moir\'e superlattice Hamiltonian, motivated by flat bands twisted bilayer graphene in perpendicular magnetic field. In doing so, address extent which these survive systems analyze nature transition. Through use Peierls substitution, determine Landau-level splitting for structure Chern range flux per plaquette. identify topological spectrum at low...

Wannier tight-binding models are effective constructed from first-principles calculations. As such, they bridge a gap between the accuracy of calculations and computational simplicity models. In this work, we extend existing methodology creating by introducing symmetrization post-processing step, which enables production Wannier-like that respect symmetries considered crystal. Furthermore, implement automatic workflows, allow for producing large number classes chemically structurally similar...

Topological semimetals with different types of band crossings provide a rich platform to realize novel fermionic excitations, known as topological fermions. In particular, some excitations can be direct analogues elementary particles in quantum field theory when both obey the same laws physics low-energy limit. Examples include Dirac and Weyl fermions, whose solid-state realizations have provided new insights into long-sought phenomena high-energy physics. Recently, theorists predicted...

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 that it anisotropic negative variety. We study effect magnetic fields on band structure topology by applying Zeeman splitting. In absence a field, we find weak topological insulators, which agreement with previous...

Transport measurements are performed on InAs/GaSb double quantum wells at zero and finite magnetic fields applied parallel perpendicular to the wells. We investigate a sample in inverted regime where electrons holes coexist, compare it with another noninverted semiconducting regime. The activated behavior conjunction strong suppression of resistance peak charge neutrality point field attest topological hybridization gap between electron hole bands sample. observe an unconventional Landau...