Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory

Eli Fonseca; Jacob Shapiro; Ahmed Sheta; Angela Wang; Kohtaro Yamakawa

doi:10.1007/s11040-020-09342-6

Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory

Eli Fonseca, Jacob Shapiro, Ahmed Sheta, Angela Wang, Kohtaro Yamakawa

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant, define a new one for the edge, and show their equivalence (the bulk-edge correspondence) via homotopy.

Original language	English (US)
Article number	29
Journal	Mathematical Physics Analysis and Geometry
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s11040-020-09342-6
State	Published - Sep 1 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematical Physics
Geometry and Topology

Keywords

Fredholm theory
Time-reversal
Topological insulators
Z invariants

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10.1007/s11040-020-09342-6

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abstract = "We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant, define a new one for the edge, and show their equivalence (the bulk-edge correspondence) via homotopy.",

keywords = "Fredholm theory, Time-reversal, Topological insulators, Z invariants",

author = "Eli Fonseca and Jacob Shapiro and Ahmed Sheta and Angela Wang and Kohtaro Yamakawa",

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AU - Fonseca, Eli

AU - Shapiro, Jacob

AU - Sheta, Ahmed

AU - Wang, Angela

AU - Yamakawa, Kohtaro

PY - 2020/9/1

Y1 - 2020/9/1

N2 - We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant, define a new one for the edge, and show their equivalence (the bulk-edge correspondence) via homotopy.

AB - We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant, define a new one for the edge, and show their equivalence (the bulk-edge correspondence) via homotopy.

KW - Fredholm theory

KW - Time-reversal

KW - Topological insulators

KW - Z invariants

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M1 - 29

ER -

Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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