Chiral symmetry and the orbital susceptibility of disordered honeycomb flakes
Abstract
The orbital susceptibility of a small disordered grain is dominated by rare samples in which an occupied and an empty level nearly touch. In a chaotic grain such near-degeneracies are suppressed by level repulsion and must also coincide with the chemical potential, so the mean susceptibility stays finite. In a neutral honeycomb flake, chiral (sublattice) symmetry removes the second condition: It places the chemical potential in the middle of the smallest gap, in every disorder realization. Here we show that the mean orbital susceptibility then grows as ln(1/T) at low temperature T if disorder can close this gap while a magnetic field still mixes the two levels, and that the hopping geometry decides whether it can: Positive nearest-neighbor hopping on a compact hexagonal flake keeps the gap open, third-neighbor hopping allows it to close. In a chiral random-matrix model with n level pairs the coefficient of the logarithm is Cn=√(2/n) Γ[(n+1)/2]/Γ(n/2), close to unity, and a detuned chemical potential cuts the logarithm off.
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BibTeX
@misc{murzaliev2026chiral,
title = {{Chiral symmetry and the orbital susceptibility of disordered honeycomb flakes}},
author = {B. Murzaliev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25555},
eprint = {2610.25555},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25555},
}
RIS
TY - UNPB
TI - Chiral symmetry and the orbital susceptibility of disordered honeycomb flakes
AU - B. Murzaliev
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25555
UR - https://arxiv.org/abs/2610.25555
AB - The orbital susceptibility of a small disordered grain is dominated by rare samples in which an occupied and an empty level nearly touch. In a chaotic grain such near-degeneracies are suppressed by level repulsion and must also coincide with the chemical potential, so the mean susceptibility stays finite. In a neutral honeycomb flake, chiral (sublattice) symmetry removes the second condition: It places the chemical potential in the middle of the smallest gap, in every disorder realization. Here we show that the mean orbital susceptibility then grows as ln(1/T) at low temperature T if disorder can close this gap while a magnetic field still mixes the two levels, and that the hopping geometry decides whether it can: Positive nearest-neighbor hopping on a compact hexagonal flake keeps the gap open, third-neighbor hopping allows it to close. In a chiral random-matrix model with n level pairs the coefficient of the logarithm is C_n=√(2/n) Γ[(n+1)/2]/Γ(n/2), close to unity, and a detuned chemical potential cuts the logarithm off.
ER -