• Open Access

Theory of competing charge density wave, Kekulé, and antiferromagnetically ordered fractional quantum Hall states in graphene aligned with boron nitride

Suraj S. Hegde and Inti Sodemann Villadiego
Phys. Rev. B 105, 195417 – Published 16 May 2022

Abstract

We investigate spin- and valley-symmetry-broken fractional quantum Hall phases within a formalism that naturally extends the paradigm of quantum Hall ferromagnetism from integer to fractional quantum Hall states, allowing us to construct detailed phase diagrams for a large class of multicomponent states. Motivated by recent experiments on graphene aligned with a boron nitride substrate, we predict a sequence of transitions realized by increasing the magnetic field, starting from a sublattice polarized state to a valley coherent Kekulé charge density wave state and further to an antiferromagnetic phase. Moreover, for filling fractions such as ν=±13, we predict that the system undergoes a transition at low fields, that not only differ by the spin-valley orientation of the fractionally filled flavors, but also by their intrinsic fractional quantum Hall nature. This transition is from a Laughlin-type state to a two-component Halperin-type state both with a charge density wave order. Moreover, for ν=±13,±23, we predict a “canted Kekulé density phase” where the spinors of integer and fractionally occupied components have different orientations in the valley Bloch sphere, in contrast to the Kekulé state for the integer quantum Hall state at neutrality where both occupied components have the same orientation in the valley Bloch sphere.

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  • Received 8 February 2022
  • Revised 16 April 2022
  • Accepted 28 April 2022

DOI:https://doi.org/10.1103/PhysRevB.105.195417

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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Suraj S. Hegde1,2,* and Inti Sodemann Villadiego3,2,†

  • 1Institut für Theoretische Physik, Technische Universität Dresden, 01069 Dresden, Germany
  • 2Max-Planck Institut für Physik Komplexer Systeme, Nöthnitzer straße 38, 01187 Dresden, Germany
  • 3Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103, Leipzig, Germany

  • *suraj.hegde@tu-dresden.de
  • sodemann@uni-leipzig.de

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Issue

Vol. 105, Iss. 19 — 15 May 2022

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