Related papers: Topological Classification of Insulators: I. Non-i…
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…
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${\bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we…
The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a…
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry.…
A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic…
The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in…
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…
We discuss a topological classification of insulators and superconductors in the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using…
Topological materials are of great interest for applications in quantum computing, providing intrinsic robustness against environmental noises. A popular direction is to look for Majorana modes in integrated systems interfaced with…
Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states…
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…
The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…
We study superconductors with $n$-fold rotational invariance both in the presence and in the absence of spin-orbit interactions. More specifically, we classify the non-interacting Hamiltonians by defining a series of $Z$-numbers for the…
We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…
The past decade has witnessed significant progress in topological materials investigation. Symmetry-indicator theory and topological quantum chemistry provide an efficient scheme to diagnose topological phases from only partial information…
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 define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these…
Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the…