### 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 language | English (US) |
---|---|

Article number | 205120 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 92 |

Issue number | 20 |

DOIs | |

State | Published - Nov 19 2015 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*92*(20), [205120]. https://doi.org/10.1103/PhysRevB.92.205120

}

*Physical Review B - Condensed Matter and Materials Physics*, vol. 92, no. 20, 205120. https://doi.org/10.1103/PhysRevB.92.205120

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

Research output: Contribution to journal › Article

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.

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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 -