• Open Access

Emergence of Dirac composite fermions: Dipole picture

Guangyue Ji and Junren Shi
Phys. Rev. Research 3, 043055 – Published 21 October 2021

Abstract

Composite fermions (CFs) are the particles underlying the novel phenomena observed in partially filled Landau levels. Both microscopic wave functions and semiclassical dynamics suggest that a CF is a dipole consisting of an electron and a double 2h/e quantum vortex, and its motion is subject to a Berry curvature that is uniformly distributed in the momentum space. Based on the picture, we study the electromagnetic response of composite fermions. We find that the response in the long-wavelength limit has a form identical to that of the Dirac CF theory. To obtain the result, we show that the Berry curvature contributes a half-quantized Hall conductance, which, notably, is independent of the filling factor of a Landau level and not altered by the presence of impurities. The latter is because CFs undergo no side-jumps when scattered by quenched impurities in a Landau-level with the particle-hole symmetry. The remainder of the response is from an effective system that has the same Fermi wave vector, effective density, Berry phase, and therefore long-wavelength response to electromagnetic fields as a Dirac CF system. By interpreting the half-quantized Hall conductance as a contribution from a redefined vacuum, we can explicitly show the emergence of a Dirac CF effective description from the dipole picture. We further determine corrections due to electric quadrupoles and magnetic moments of CFs and show deviations from the Dirac CF theory when moving away from the long-wavelength limit.

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  • Received 5 July 2021
  • Revised 28 September 2021
  • Accepted 29 September 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.043055

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Guangyue Ji1 and Junren Shi1,2,*

  • 1International Center for Quantum Materials, Peking University, Beijing 100871, China
  • 2Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

  • *junrenshi@pku.edu.cn

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Issue

Vol. 3, Iss. 4 — October - December 2021

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