Anomalous transport gaps of fractional quantum Hall phases in graphene Landau levels are induced by spin-valley entangled ground states

Jincheng An; Ajit C. Balram; Udit Khanna; Ganpathy Murthy

doi:10.1103/rth3-mkpl

Anomalous transport gaps of fractional quantum Hall phases in graphene Landau levels are induced by spin-valley entangled ground states

Jincheng An
, Ajit C. Balram
, Udit Khanna
, Ganpathy Murthy

Research output: Contribution to journal › Article › peer-review

Abstract

We evaluate the transport gaps in the most prominent fractional quantum Hall states in the n = 0 and n = 1 Landau levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body terms. We find that the fractional phases in the n = 0 Landau level are bond ordered, while those in the n = 1 Landau level are spin-valley entangled. This resolves a long-standing experimental puzzle [F. Amet et al., Nat. Commun. 6, 5838 (2015)] of the contrasting Zeeman dependence of the transport gaps in the two Landau levels. The spin-valley entangled phases host gapless Goldstone modes that can be probed via bulk thermal transport measurements. As a byproduct of our computations, we place strong constraints on the values of the microscopic anisotropic couplings such that these are consistent with all known experimental results.

Original language	English
Pages (from-to)	1154181-11541811
Number of pages	10387631
Journal	Physical Review B
Volume	112
Issue number	11
DOIs	https://doi.org/10.1103/rth3-mkpl
State	Published - Sep 12 2025

Bibliographical note

Publisher Copyright:
© 2025 American Physical Society

Funding

J.A. and G.M. are partially supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0024346. J.A. is also grateful to the University of Kentucky Center for Computational Sciences and Information Technology Services Research Computing for allowing the use of the Morgan Compute Cluster. U.K. acknowledges support from the Department of Space (DOS), Government of India. We acknowledge the Science and Engineering Research Board (SERB) of the Department of Science and Technology (DST) for financial support through the Mathematical Research Impact Centric Support (MATRICS) Grant No. MTR/2023/000002. Some of the numerical calculations reported in this work were carried out on the Nandadevi and Kamet supercomputers, which are maintained and supported by the Institute of Mathematical Science’s High-Performance Computing Center. Some numerical calculations were performed using the DIAGHAM libraries [66], for which we are grateful to the authors.

Funders	Funder number
Science and Engineering Research Board
Institute of Mathematical Sciences India
Indian Space Research Organisation
U.S. Department of Energy
Office of Science Programs
Kentucky Transportation Center, University of Kentucky
DOE Basic Energy Sciences	DE-SC0024346
Department of Science and Technology, Ministry of Science and Technology, India	MTR/2023/000002

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics

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Cite this

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AB - We evaluate the transport gaps in the most prominent fractional quantum Hall states in the n = 0 and n = 1 Landau levels of graphene, accounting for the Coulomb interaction, lattice-scale anisotropies, and one-body terms. We find that the fractional phases in the n = 0 Landau level are bond ordered, while those in the n = 1 Landau level are spin-valley entangled. This resolves a long-standing experimental puzzle [F. Amet et al., Nat. Commun. 6, 5838 (2015)] of the contrasting Zeeman dependence of the transport gaps in the two Landau levels. The spin-valley entangled phases host gapless Goldstone modes that can be probed via bulk thermal transport measurements. As a byproduct of our computations, we place strong constraints on the values of the microscopic anisotropic couplings such that these are consistent with all known experimental results.

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Anomalous transport gaps of fractional quantum Hall phases in graphene Landau levels are induced by spin-valley entangled ground states

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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