Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Dragoljub Gočanin, Sonja Predin, Marija Dimitrijević Ćirić, Voja Radovanović, and Milica Milovanović
Phys. Rev. B 104, 115150 – Published 23 September 2021

Abstract

Building on previous work [N. Read, Phys. Rev. B 58, 16262 (1998); Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor ν=1, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and apply the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling p-wave pairing in the lowest Landau level, and strong coupling p-wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.

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  • Received 2 March 2021
  • Revised 3 August 2021
  • Accepted 15 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.115150

©2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dragoljub Gočanin1, Sonja Predin2, Marija Dimitrijević Ćirić1, Voja Radovanović1, and Milica Milovanović3,*

  • 1Faculty of Physics, University of Belgrade, Studentski Trg 12-16, 11000 Belgrade, Serbia
  • 2Institute of Information Systems, Alfons-Goppel-Platz 1, 95030 Hof, Germany
  • 3Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

  • *Corresponding author: milica.milovanovic@ipb.ac.rs

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Issue

Vol. 104, Iss. 11 — 15 September 2021

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