46 citations · 63 across the 5 of their papers we have counts for
5 papers
An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
Shin Hayashi
In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg-Krein theory for matrix…
Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
Yuki Nagasato, Yositake Takane, Yukinori Yoshimura +2
A second-order topological insulator on a two-dimensional square lattice hosts zero-dimensional states inside a band gap. They are localized near and cor…
Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
Shin Hayashi
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theor…
Bulk-edge correspondence and the cobordism invariance of the index
Shin Hayashi
We show that the bulk-edge correspondence for two-dimensional type A and type AII topological insulators follows directly from the cobordism invariance of the index.
Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c Manifolds
Shin Hayashi
An integer valued topological index of a Dirac operator is introduced for a pair of a 4n+2 dimensional open Spin^c manifold and a section of the determinant line bundle satisfying…