Index Theorems, Generalized Hall Currents, and Topology for Gapless Defect Fermions

Kaplan, David B.; Sen, Srimoyee

doi:10.1103/physrevlett.128.251601

Index Theorems, Generalized Hall Currents, and Topology for Gapless Defect Fermions

Journal Article · Tue Jun 21 00:00:00 EDT 2022 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.128.251601· OSTI ID:1903228

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Univ. of Washington, Seattle, WA (United States); Iowa State University
Iowa State Univ., Ames, IA (United States)

In this work, we show how the index of the fermion operator from the Euclidean action can be used to uncover the existence of gapless modes living on defects (such as edges and vortices) in topological insulators and superconductors. The 1-loop Feynman diagram that computes the index reveals an analog of the quantum Hall current flowing on and off the defect—even in systems without conserved currents or chiral anomalies—and makes explicit the interplay between topology in momentum and coordinate space. We provide several explicit examples.

View Accepted Manuscript (DOE)

Research Organization:: Iowa State Univ., Ames, IA (United States); Univ. of Washington, Seattle, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-00ER41132; SC0021892

OSTI ID:: 1903228

Alternate ID(s):: OSTI ID: 1922431

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 25 Vol. 128; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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