相关论文: Crystallographic bulk-edge correspondence: glide r…

Most natural and artificial materials have crystalline structures from which abundant topological phases emerge [1-6]. The bulk-edge correspondence, widely-adopted in experiments to determine the band topology from edge properties, however,…

We propose a theory, that we call the \textit{mode-shell correspondence}, which relates the topological zero-modes localised in phase space to a \textit{shell} invariant defined on the surface forming a shell enclosing these zero-modes. We…

We study bulk/edge aspects of continuous honeycomb lattices in a magnetic field. We compute the bulk index of Bloch eigenbundles: it equals $2$ or $-2$, with sign depending on nearby Dirac points and on the magnetic field. We then prove the…

We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the…

The bulk-edge correspondence characterizes topological insulators and superconductors. We generalize this concept to the bulk-corner correspondence and the edge-corner correspondence in two dimensions. In the bulk-corner (edge-corner)…

The correspondence between the edge theory and the entanglement spectrum is firmly established for the chiral topological phases. We study gapped, topologically ordered, non-chiral states with a conserved $U(1)$ charge and show that the…

In a finite one-dimensional non-Hermitian system, the number of zero modes does not necessarily reflect the topology of the system. This is known as the breakdown of the bulk-boundary correspondence and has led to misconceptions about the…

The synergy of non-Hermitian and topology renders the bulk-boundary correspondence (BBC) even more elusive. Here we study a non-Hermitian Creutz ladder that incorporates both gain-loss and nonreciprocity, and construct multiple BBCs…

We present microscopic Hamiltonians that gap the Dirac fermions on the surface of topological crystalline insulators (TCIs) protected by reflection symmetry and create symmetry-preserving states with Abelian topological orders. For TCIs…

Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle-hole symmetry can open up new possibilities for topological phenomena in classical systems. Here…

Topological insulators, along with Chern insulators and Quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. This article reports the experimental realization of the time-reversal…

Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that…

Recently, there is an interest in studying the bulk-edge correspondence for nonlinear eigenvalues problems in a two-dimensional topological system with spin-orbit coupling. By introducing auxiliary eigenvalues, the nonlinear bulk-edge…

We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and…

We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the…

Existence of nontrivial topological phases in a tight binding Haldane-like model on the depleted Lieb lattice is reported. This two-band model is formulated by considering the nearest-neighbor, next-nearest-neighbor and…

We study the Dirac Hamiltonian in dimension two with a mass term and a large momentum regularization, and show that bulk-edge correspondence fails. Despite a well defined bulk topological index --the Chern number--, the number of edge modes…

We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear…

The boundary of topological phases of matter can manifest its topology nature, which leads to the so-called boundary-bulk correspondence (BBC) of topological phases. In this Letter, we construct a one-to-one correspondence between the…

We propose a Z$_2$ index theorem for a generic topological superconductor in class D. Introducing a particle-hole symmetry breaking term depending on a parameter and regarding it as a coordinate of an extra dimension, we define the index of…