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

David B Kaplan1, Srimoyee Sen2

  • 1Institute for Nuclear Theory, University of Washington, Box 351550, Seattle, Washington 98195-1550, USA.

Physical Review Letters
|July 8, 2022
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Summary
This summary is machine-generated.

The fermion operator index reveals gapless modes on defects in topological materials. This method uncovers quantum Hall-like currents on edges and vortices, even without conserved currents.

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Area of Science:

  • Condensed matter physics
  • Topological materials science

Background:

  • Topological insulators and superconductors host unique electronic states.
  • Understanding boundary phenomena is crucial for topological material applications.

Purpose of the Study:

  • To demonstrate a novel method for detecting gapless modes on defects.
  • To connect topological properties in momentum and real space.

Main Methods:

  • Utilizing the index of the fermion operator derived from the Euclidean action.
  • Analyzing 1-loop Feynman diagrams to compute the topological index.
  • Investigating systems with and without conserved currents or chiral anomalies.

Main Results:

  • The fermion operator index successfully identifies gapless modes on defects like edges and vortices.
  • A quantum Hall current analog is observed flowing on and off these defects.
  • The method explicitly reveals the interplay between momentum-space and real-space topology.

Conclusions:

  • The fermion operator index provides a powerful tool for uncovering defect-localized topological states.
  • This approach offers new insights into the behavior of topological materials at boundaries.
  • The findings are applicable to various topological systems, including insulators and superconductors.