Generalization of spectral bulk-boundary correspondence

Abstract

The bulk-boundary correspondence in one dimension asserts that the physical quantities defined in the bulk and at the edge are connected, as well established in the argument for electric polarization. Recently, a spectral bulk-boundary correspondence (SBBC), an extended version of the conventional bulk-boundary correspondence to energy-dependent spectral functions, such as Green's functions, has been proposed in chiral symmetric systems, in which the chiral operator anticommutes with the Hamiltonian. In this study, we extend the SBBC to a system with impurity scattering and dynamical self-energies, regardless of the presence or absence of a gap in the energy spectrum. Moreover, the SBBC is observed to hold even in a system without chiral symmetry, which substantially generalizes its concept. The SBBC is demonstrated with concrete models, such as superconducting nanowires and a normal metallic chain. Its potential applications and certain remaining issues are also discussed.

Bulk-boundary correspondence in topological systems with the momentum dependent energy shift

“…One of the most typical ways to characterize topological nontrivial states of matter is achieved via the bulk topological invariants obtained with periodical boundary conditions. Conventionally, preserved bulk-boundary correspondence (BBC) suggests that non-vanishing bulk topological invariants indicate the presence of nontrivial edge modes in open boundary conditions [18][19][20][21].…”

Non-Hermitian Floquet topological phases in one-dimensional system

“…In recent years, the non-Hermitian Floquet phase has been at the forefront of condensed matter physics [1][2][3][4][5][6][7][8]. These Floquet topological phases are characterized by topological invariants, bulk-boundary correspondence [9][10][11][12][13][14][15][16]. Under appropriate designed driving fields, The Floquet topological phase can be generated, and leads to some interesting phenomena.…”