Spontaneous polarization of composite fermions in the n=1 Landau level of graphene

Ajit C. Balram, Csaba Toke, A. Wójs, Jainendra K. Jain

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Motivated by recent experiments that reveal expansive fractional quantum Hall states in the n=1 graphene Landau level and suggest a nontrivial role of the spin degree of freedom [31F. Amet, A. J. Bestwick, J. R. Williams, L. Balicas, K. Watanabe, T. Taniguchi, and D. Goldhaber-Gordon, Nat. Commun. 6, 5838 (2015)2041-172310.1038/ncomms6838], we perform an accurate quantitative study of the competition between fractional quantum Hall states with different spin polarizations in the n=1 graphene Landau level. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the n=0 Landau level. In particular, for the states at filling factors ν=s/(2s±1), s positive integer, a combination of exact diagonalization and the composite fermion theory shows that the ground state is fully spin polarized and supports a robust spin-wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean-field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin-polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the n=1 graphene Landau level, indicating an absence of composite fermion pairing at half filling in the n=1 graphene Landau level.

Original languageEnglish (US)
Article number205120
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume92
Issue number20
DOIs
StatePublished - Nov 19 2015

Fingerprint

Graphite
Fermions
Graphene
graphene
fermions
Polarization
composite materials
Composite materials
polarization
Spin polarization
Quantum Hall effect
Spin waves
Exchange interactions
Ground state
quantum Hall effect
Physics
magnons
integers
degrees of freedom
breakdown

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

@article{9b1e8173427b469ba98b268ce84da341,
title = "Spontaneous polarization of composite fermions in the n=1 Landau level of graphene",
abstract = "Motivated by recent experiments that reveal expansive fractional quantum Hall states in the n=1 graphene Landau level and suggest a nontrivial role of the spin degree of freedom [31F. Amet, A. J. Bestwick, J. R. Williams, L. Balicas, K. Watanabe, T. Taniguchi, and D. Goldhaber-Gordon, Nat. Commun. 6, 5838 (2015)2041-172310.1038/ncomms6838], we perform an accurate quantitative study of the competition between fractional quantum Hall states with different spin polarizations in the n=1 graphene Landau level. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the n=0 Landau level. In particular, for the states at filling factors ν=s/(2s±1), s positive integer, a combination of exact diagonalization and the composite fermion theory shows that the ground state is fully spin polarized and supports a robust spin-wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean-field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin-polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the n=1 graphene Landau level, indicating an absence of composite fermion pairing at half filling in the n=1 graphene Landau level.",
author = "Balram, {Ajit C.} and Csaba Toke and A. W{\'o}js and Jain, {Jainendra K.}",
year = "2015",
month = "11",
day = "19",
doi = "10.1103/PhysRevB.92.205120",
language = "English (US)",
volume = "92",
journal = "Physical Review B-Condensed Matter",
issn = "1098-0121",
publisher = "American Physical Society",
number = "20",

}

Spontaneous polarization of composite fermions in the n=1 Landau level of graphene. / Balram, Ajit C.; Toke, Csaba; Wójs, A.; Jain, Jainendra K.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 92, No. 20, 205120, 19.11.2015.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Spontaneous polarization of composite fermions in the n=1 Landau level of graphene

AU - Balram, Ajit C.

AU - Toke, Csaba

AU - Wójs, A.

AU - Jain, Jainendra K.

PY - 2015/11/19

Y1 - 2015/11/19

N2 - Motivated by recent experiments that reveal expansive fractional quantum Hall states in the n=1 graphene Landau level and suggest a nontrivial role of the spin degree of freedom [31F. Amet, A. J. Bestwick, J. R. Williams, L. Balicas, K. Watanabe, T. Taniguchi, and D. Goldhaber-Gordon, Nat. Commun. 6, 5838 (2015)2041-172310.1038/ncomms6838], we perform an accurate quantitative study of the competition between fractional quantum Hall states with different spin polarizations in the n=1 graphene Landau level. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the n=0 Landau level. In particular, for the states at filling factors ν=s/(2s±1), s positive integer, a combination of exact diagonalization and the composite fermion theory shows that the ground state is fully spin polarized and supports a robust spin-wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean-field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin-polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the n=1 graphene Landau level, indicating an absence of composite fermion pairing at half filling in the n=1 graphene Landau level.

AB - Motivated by recent experiments that reveal expansive fractional quantum Hall states in the n=1 graphene Landau level and suggest a nontrivial role of the spin degree of freedom [31F. Amet, A. J. Bestwick, J. R. Williams, L. Balicas, K. Watanabe, T. Taniguchi, and D. Goldhaber-Gordon, Nat. Commun. 6, 5838 (2015)2041-172310.1038/ncomms6838], we perform an accurate quantitative study of the competition between fractional quantum Hall states with different spin polarizations in the n=1 graphene Landau level. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the n=0 Landau level. In particular, for the states at filling factors ν=s/(2s±1), s positive integer, a combination of exact diagonalization and the composite fermion theory shows that the ground state is fully spin polarized and supports a robust spin-wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean-field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin-polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the n=1 graphene Landau level, indicating an absence of composite fermion pairing at half filling in the n=1 graphene Landau level.

UR - http://www.scopus.com/inward/record.url?scp=84949680612&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949680612&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.92.205120

DO - 10.1103/PhysRevB.92.205120

M3 - Article

AN - SCOPUS:84949680612

VL - 92

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 20

M1 - 205120

ER -