Related papers: Classification of topological insulators and super…
Quantum anomalies, breakdown of classical symmetries by quantum effects, provide a sharp definition of symmetry protected topological phases. In particular, they can diagnose interaction effects on the non-interacting classification of…
Two-dimensional (2D) model of a weak topological insulator with $N$-stacked Su-Schrieffer-Heeger (SSH) chain is studied. This study starts with a basic model with all the fundamental symmetries (chiral, time-reversal, and particle-hole)…
Topological crystalline insulators (TCI) are new topological phases of matter protected by crystal symmetry of solids. Recently, the first realization of TCI has been predicted and observed in IV-VI semiconductor SnTe and related alloys…
Topologically protected gapless edge/surface states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with…
We report appearance of non-trivial zero energy corner modes in the form of topological defects (trimers) in a carefully designed 2D crystalline topological insulator. The proposed scenario is developed via an unconventional stacking of 1D…
In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of 1D systems. We focus on the TR-invariant Majorana chain (BDI symmetry class). While the band…
We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless $\mathcal{P}\mathcal{T}$ symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases…
We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…
In this paper we introduce four Z_2 topological indices zeta_k=0,1 at k=(0,0), (0,pi), (pi, 0), (pi, pi) characterizing 16 universal classes of 2D superconducting states that have translation symmetry but may break any other symmetries. The…
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
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 further investigate a class of time-reversal-invariant two-band s-wave topological superconductors introduced in Phys. Rev. Lett. 108, 036803 (2012). We show how, in the presence of time-reversal symmetry, Z_2 invariants that distinguish…
High-order topological phases host robust boundary states at the boundary of the boundary, which can be interpreted from their boundary topology. In this work, considering the interplay between superconductors and magnetic fields to gap the…
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of…
Topological insulators are new states of quantum matter with surface states protected by the time-reversal symmetry. In this work, we perform first-principle electronic structure calculations for $Sb_2Te_3$, $Sb_2Se_3$, $Bi_2Te_3$ and…
The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac…