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PreprintCC BY 4.0arXiv

Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the 𝒩=2 Landau levels of Bernal-stacked bilayer graphene

  • Rakesh K. Dora
  • Udit Khanna
  • Ajit C. Balram
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Abstract

Bernal-stacked bilayer graphene (BLG), in which a graphene layer is stacked atop another and laterally shifted by a lattice constant, offers remarkable tunability in its single-particle states under applied magnetic and displacement fields. Owing to this tunability, recent transport and scanning tunneling microscopy experiments in the presence of a perpendicular magnetic field and finite interlayer displacement fields have observed even-denominator fractional quantum Hall (FQH) states at half-filling in the first excited, namely, 𝒩=2, Landau level (LL) of BLG. In contrast, at zero displacement field, a gapless composite fermion Fermi liquid (CFFL) is realized at half-filling of the 𝒩=2 LL. Motivated by these experiments, we compute the phase diagram as a function of the displacement field in the half-filled 𝒩=2 LL of BLG by studying the competition between the CFFL and the Moore-Read state---a candidate even-denominator FQH state---by calculating their thermodynamic energies in this setting. We find that the modified effective Coulomb interaction, induced by changes in the single-particle states with increasing displacement field, softens the inter-electronic repulsion at short distances, thereby stabilizing the Moore-Read state over the CFFL in the 𝒩=2 LL of BLG. We also study the nature of FQH states at fillings 2/5, 3/7, 4/9, and 6/13 in the 𝒩=2 LL of BLG. Our results suggest that, with increasing displacement field, the Jain composite-fermion states at 3/7, 4/9, and 6/13 transition into states with distinct topological order that are well-captured by parton wave functions.

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Cite

BibTeXRIS
BibTeX
@misc{dora2026displacement,
  title = {{Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the $\mathcalN=2$ Landau levels of Bernal-stacked bilayer graphene}},
  author = {Rakesh K. Dora and Udit Khanna and Ajit C. Balram},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19379},
  eprint = {2609.19379},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19379},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the 𝒩=2 Landau levels of Bernal-stacked bilayer graphene
AU  - Rakesh K. Dora
AU  - Udit Khanna
AU  - Ajit C. Balram
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19379
UR  - https://arxiv.org/abs/2609.19379
AB  - Bernal-stacked bilayer graphene (BLG), in which a graphene layer is stacked atop another and laterally shifted by a lattice constant, offers remarkable tunability in its single-particle states under applied magnetic and displacement fields. Owing to this tunability, recent transport and scanning tunneling microscopy experiments in the presence of a perpendicular magnetic field and finite interlayer displacement fields have observed even-denominator fractional quantum Hall (FQH) states at half-filling in the first excited, namely, 𝒩=2, Landau level (LL) of BLG. In contrast, at zero displacement field, a gapless composite fermion Fermi liquid (CFFL) is realized at half-filling of the 𝒩=2 LL. Motivated by these experiments, we compute the phase diagram as a function of the displacement field in the half-filled 𝒩=2 LL of BLG by studying the competition between the CFFL and the Moore-Read state---a candidate even-denominator FQH state---by calculating their thermodynamic energies in this setting. We find that the modified effective Coulomb interaction, induced by changes in the single-particle states with increasing displacement field, softens the inter-electronic repulsion at short distances, thereby stabilizing the Moore-Read state over the CFFL in the 𝒩=2 LL of BLG. We also study the nature of FQH states at fillings 2/5, 3/7, 4/9, and 6/13 in the 𝒩=2 LL of BLG. Our results suggest that, with increasing displacement field, the Jain composite-fermion states at 3/7, 4/9, and 6/13 transition into states with distinct topological order that are well-captured by parton wave functions.
ER  -