Generalized Hall currents in topological insulators and superconductors

Kaplan, David B.; Sen, Srimoyee

doi:10.1103/physrevd.108.045019

Title: Generalized Hall currents in topological insulators and superconductors

Journal Article · 29 August 2023 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.108.045019 · OSTI ID:2418921

Kaplan, David B. ^[1];

^[2]

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

We generalize the idea of the quantized Hall current to count gapless edge states in topological materials, applying equally well to theories in different dimensions, with or without continuous symmetries in the bulk or chiral anomalies on the boundaries. This current is related to the index of the Euclidean fermion operator and can be calculated via one-loop Feynman diagrams. Quantization of the current is shown to be governed by topology in phase space, and the procedure can be applied to topological classes governed by either Z or Z₂ invariants. We analyze several explicit examples of free fermions in relativistic field theories. We speculate that it may be possible to extend the technique to interacting theories as well, such as the interesting cases where interactions gap the edge states.

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

Sponsoring Organization:: USDOE Office of Science (SC)

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

OSTI ID:: 2418921

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 4 Vol. 108; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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