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Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials
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Skyrmions and Hall Transport.

Bom Soo Kim1, Alfred D Shapere1

  • 1Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.

Physical Review Letters
|September 24, 2016
PubMed
Summary

We developed new Ward identities linking topological charge to Hall transport. This reveals a direct connection between thermal Hall conductivity, topological charge density, and Hall viscosity in materials.

Area of Science:

  • Condensed matter physics
  • Topological physics
  • Quantum transport

Background:

  • Hall transport phenomena are crucial in condensed matter physics.
  • Topological charge and its influence on material properties are of significant interest.
  • Understanding the interplay between topology and transport is key for novel electronic devices.

Purpose of the Study:

  • To derive generalized Ward identities for topological charge effects on Hall transport.
  • To establish a direct relationship between thermal Hall conductivity and topological charge density.
  • To extend these findings to include magnetic fields, electric currents, and Hall viscosity.

Main Methods:

  • Derivation of generalized Ward identities from (2+1)-dimensional momentum algebra.

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  • Analysis of central extension in momentum algebra related to topological charge density.
  • Incorporation of topological objects like Skyrmions into the theoretical framework.
  • Extension of relations to include magnetic fields and electric currents.

    • Main Results:

    • A generalized set of Ward identities capturing topological charge effects on Hall transport was derived.
    • A direct relation between thermal Hall conductivity and topological charge density was found in the presence of Skyrmions.
    • Topological charge density shows a distinct signature in electric Hall conductivity, matching experimental data and predicting new phenomena.
    • Hall viscosity in insulating materials was directly linked to Skyrmion density and thermal Hall conductivity.

    Conclusions:

    • The derived Ward identities provide a powerful tool for understanding topological charge in Hall transport.
    • Topological charge density offers a unique signature in Hall conductivity, with implications for experimental verification and discovery.
    • The study establishes a direct link between microscopic topological features and macroscopic transport coefficients like Hall viscosity.