Theory of local $\mathbb{Z}_{2}$ topological markers for finite and periodic two-dimensional systems

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Baù, Nicolas, Marrazzo, Antimo
Formato: Preprint
Publicado: 2024
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866929487015313408
author Baù, Nicolas
Marrazzo, Antimo
author_facet Baù, Nicolas
Marrazzo, Antimo
contents The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts in reciprocal space, hence implicitly assuming periodicity and homogeneity. Here, we introduce two space-resolved $\mathbb{Z}_{2}$ topological markers that are able to probe the local topology of the ground-state electronic structure also in the case of inhomogeneous and finite systems. The first approach leads to a generalized local spin-Chern marker, that usually remains well-defined also when the perpendicular component of the spin, $S_{z}$, is not conserved. The second marker is solely based on time-reversal symmetry, hence being more general. We validate our markers on the Kane-Mele model both in periodic and open boundary conditions, also in presence of disorder and including topological/trivial heterojunctions.
format Preprint
id arxiv_https___arxiv_org_abs_2404_04598
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Theory of local $\mathbb{Z}_{2}$ topological markers for finite and periodic two-dimensional systems
Baù, Nicolas
Marrazzo, Antimo
Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Materials Science
The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts in reciprocal space, hence implicitly assuming periodicity and homogeneity. Here, we introduce two space-resolved $\mathbb{Z}_{2}$ topological markers that are able to probe the local topology of the ground-state electronic structure also in the case of inhomogeneous and finite systems. The first approach leads to a generalized local spin-Chern marker, that usually remains well-defined also when the perpendicular component of the spin, $S_{z}$, is not conserved. The second marker is solely based on time-reversal symmetry, hence being more general. We validate our markers on the Kane-Mele model both in periodic and open boundary conditions, also in presence of disorder and including topological/trivial heterojunctions.
title Theory of local $\mathbb{Z}_{2}$ topological markers for finite and periodic two-dimensional systems
topic Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Materials Science
url https://arxiv.org/abs/2404.04598