Related papers: A New Numerical Method for $\mathbb{Z}_2$ Topologi…
We present an approach for the calculation of the $\mathbb{Z}_2$ topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline…
Topological indices are graph invariants numeric quantities, which are utilized by researchers to analyze a variety of physiochemical aspects of molecules. The goal of developing topological indices is to give each chemical structure a…
We study topological insulators under dephasing noise. With examples of both a $2d$ Chern insulator and a $3d$ topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing…
The symmetry-based indicator [H. C. Po, A. Vishwanath, H. Watanabe, Nat. Commun. 8, 50 (2017)] is a practical tool to diagnose topological materials in the band theory. In this note, we present two directions to generalize the…
It has recently been shown that crystalline defects - dislocation lines - in three dimensional topological insulators, can host protected one dimensional modes propagating along their length. We generalize this observation to the case of…
Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of…
Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…
Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to…
We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time reversal symmetry in the presence of interactions. For a closed geometry, Fidkowski and Kitaev have shown…
Usually $Z_2$ topological insulators are protected by time reversal symmetry. Here, we present a new type of $Z_2$ topological insulators in a cubic lattice which is protected by a novel hidden symmetry, while time reversal symmetry is…
Using the method of noncommutative geometry, we define a topological invariant in disordered bosonic Bogoliubov-de Gennes systems, which possess a unique mathematical property---non-Hermiticity. To demonstrate the validity of the…
Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the…
We describe how optical dressing can be used to generate bandstructures for ultracold atoms with non-trivial Z_2 topological order. Time reversal symmetry is preserved by simple conditions on the optical fields. We first show how to…
We study the effects of temperature on the topological nature of ZrTe$_5$, which sits near the phase boundary between strong and weak topological insulating orders. Using first-principles calculations, we show that the band gap and the…
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…
Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be continuously connected to the clean limit and are therefore genuinely disorder-driven. We demonstrate this in…
We study interaction induced topological phase transition in Bernevig-Hughes-Zhang model. Topological nature of the phase transition is revealed by directly calculating the Z2 index of the interacting system from the single-particle Green's…
This review deals with strongly disordered topological insulators and covers some recent applications of a well established analytic theory based on the methods of Non-Commutative Geometry (NCG) and developed for the Integer Quantum…
In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be symplectic. This…
We review Kitaev's celebrated "periodic table" for topological phases of condensed matter, which identifies ground states (Fermi projections) of gapped periodic quantum systems up to continuous deformations. We study families of projections…