Related papers: Global band topology of simple and double Dirac-po…
We present the exhaustive classification of surface states of topological insulators and superconductors protected by crystallographic magnetic point group symmetry in three spatial dimensions. Recently, Cornfeld and Chapman [Phys. Rev. B…
We performed angle-resolved photoelectron spectroscopy of the Bi(111) surface to demonstrate that this surface support edge states of non-trivial topology. Along the $\bar{\Gamma}\bar{M}$-direction of the surface Brillouin zone, a…
Recent development in exact classification of a superconducting gap has elucidated various unconventional gap structures, which have not been predicted by the classification of order parameter based on the point group. One of the important…
We theoretically study three-dimensional topological semimetals (TSMs) with nodal lines protected by crystalline symmetries. Compared with TSMs with point nodes, e.g., Weyl semimetals and Dirac semimetals, where the conduction and the…
We have investigated the band structure at the $\Gamma$ point of the three-dimensional (3D) topological insulator Bi$_2$Se$_3$ using magneto-spectroscopy over a wide range of energies ($0.55-2.2$\,eV) and in ultrahigh magnetic fields up to…
We consider a tight-binding model defined by a matrix Hamiltonian over 2D Brillouin zone. Multiband energy spectrum gives rise to a non-Abelian gauge structure set by the Berry connections. The corresponding curvature $F_{\mu\nu}$ vanishes…
The manipulation and movement of Dirac points in the Brillouin zone by the electron-electron interaction is considered within leading order perturbation theory. At the merging point, an infinitesimal interaction is shown to cause opening of…
We present a new type of three-dimensional essential Dirac semimetal with magnetic ordering. The Dirac points are protected by the magnetic space groups and cannot be gapped without lowering such symmetries, where the combined antiunitary…
Crystallographic symmetries enforcing band touchings (BTs) in the Brillouin zone (BZ) have been utilized to classify and predict the topological semimetals. Though the early proposed topological semimetals contain isolated nodal points in…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from overlap Dirac operator organizes into an ordered space-time structure. It was…
We study the occurrence of symmetry-enforced topological band crossings in tetragonal crystals with strong spin-orbit coupling. By computing the momentum dependence of the symmetry eigenvalues and the global band topology in the entire…
In a Dirac semimetal, the conduction and valence bands contact only at discrete (Dirac) points in the Brillouin zone (BZ) and disperse linearly in all directions around these critical points. Including spin, the low energy effective theory…
We study the stability of gap-closing (Weyl or Dirac) points in the three-dimensional Brillouin zone of semimetals using Clifford algebras and their representation theory. We show that a pair of Weyl points with $\mathbb{Z}_2$ topological…
The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone. Since the discovery of topological insulators, much attention has been paid to the…
We present a general methodology towards the systematic characterization of crystalline topological insulating phases with time reversal symmetry (TRS).~In particular, taking the two-dimensional spinful hexagonal lattice as a proof of…
We present a detailed study of the gap symmetry and the quasiparticle wave function topology in two-dimensional superconductors without inversion center. The strong spin-orbit coupling of electrons with the crystal lattice makes it…
We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and…
Many systems are topologically trivial in the bulk, but still have non-trivial wavefunctions locally in the Brillouin zone. For example, in a small-gap Dirac material the Berry curvature is strongly peaked, but cancels over the full…
The band inversions that generate the topologically non-trivial band gaps of topological insulators and the isolated Dirac touching points of three-dimensional Dirac semimetals generally arise from the crossings of electronic states derived…