相关论文: Equivalence of Topological Insulators and Supercon…
We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path…
The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. Among these, the Kitaev model of a one-dimensional $p$-wave superconductor plays a guiding…
Supersymmetry, originally proposed in particle physics, refers to a dual relation that connects fermionic and bosonic degrees of freedom in a system. Recently, there has been considerable interest in applying the idea of supersymmetry to…
Motivated by the InSb nanowire superconductor system, we investigate a system where one-dimensional topological superconductors are placed in parallel. It would be simulated well by a ladder of the Kitaev chains. The system undergoes…
The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically…
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…
Crystalline symmetry and time-reversal symmetry are commonly present in real superconducting materials. However, the topological classification of systems respecting these symmetries, particularly for interacting fermions, remains…
We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of…
We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion…
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 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 a new class of materials which have gapped spectra in the bulk, but are accompanied by topologically protected gapless excitations at the surface (edge) of the system. These phenomena have a close relationship…
After briefly recalling the quantum entanglement-based view of topological phases of matter in order to outline the general context, we give an overview of different approaches to the classification problem of topological insulators and…
We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of…
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly…
Three-dimensional topological insulators can be described by an effective field theory involving two `hydrodynamic' Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes…
Although classification for free-fermion topological superconductors (TSC) is established, systematically understanding the classification of 3D interacting TSCs remains difficult, especially those protected by crystalline symmetries like…
We initiate the study of the effects of strongly-coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time reversal…
Electric-magnetic duality ($S$-duality) is a well-known property of pure $u(1)$ gauge theory in 3+1 dimensions. In this paper, we investigate the compatibility of this duality with time-reversal symmetry. We consider two theories obtained…
We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic…