Magnetoconductivity of two-dimensional Dirac cones and gapped nodal-rings under impurity-potentials in the ultraquantum limit
Abstract
We investigate the dc magnetoconductivity of two-dimensional Dirac cones and gapped nodal rings (GNRs) subjected to a perpendicular magnetic field, which quantises the electronic spectrum into Landau levels (LLs). Working in the ultraquantum limit, where only the lowest LL (LLL) is partially occupied, we employ the Kubo--Bastin formalism to compute the transport coefficients for pointlike, Gaussian, and Yukawa impurity-potentials. For the Dirac case, the longitudinal conductivity is field-independent for pointlike impurities and a monotonic function of B for the Gaussian and Yukawa potentials, while the Hall conductivity vanishes identically owing to the particle-hole symmetry of the two neighbouring LLs. The GNR case is qualitatively different: its non-monotonic stretched-checkmark LL spectrum causes the effective LLL to migrate to successively lower indices as the field increases, producing a pronounced oscillatory structure in both conductivities. The longitudinal response develops resonant peaks at LLL degeneracies, while the Hall conductivity traces out a sawtooth pattern with sharp zero-crossings at these same points. These results establish distinct transport fingerprints for the two systems in the extreme quantum limit, and provide a theoretical framework for interpreting magnetotransport experiments on GNRs.
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BibTeX
@misc{mandal2026magnetoconductivity,
title = {{Magnetoconductivity of two-dimensional Dirac cones and gapped nodal-rings under impurity-potentials in the ultraquantum limit}},
author = {Ipsita Mandal and Sanskar Sharma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.18769},
eprint = {2607.18769},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18769},
}
RIS
TY - UNPB
TI - Magnetoconductivity of two-dimensional Dirac cones and gapped nodal-rings under impurity-potentials in the ultraquantum limit
AU - Ipsita Mandal
AU - Sanskar Sharma
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2607.18769
UR - https://arxiv.org/abs/2607.18769
AB - We investigate the dc magnetoconductivity of two-dimensional Dirac cones and gapped nodal rings (GNRs) subjected to a perpendicular magnetic field, which quantises the electronic spectrum into Landau levels (LLs). Working in the ultraquantum limit, where only the lowest LL (LLL) is partially occupied, we employ the Kubo--Bastin formalism to compute the transport coefficients for pointlike, Gaussian, and Yukawa impurity-potentials. For the Dirac case, the longitudinal conductivity is field-independent for pointlike impurities and a monotonic function of B for the Gaussian and Yukawa potentials, while the Hall conductivity vanishes identically owing to the particle-hole symmetry of the two neighbouring LLs. The GNR case is qualitatively different: its non-monotonic stretched-checkmark LL spectrum causes the effective LLL to migrate to successively lower indices as the field increases, producing a pronounced oscillatory structure in both conductivities. The longitudinal response develops resonant peaks at LLL degeneracies, while the Hall conductivity traces out a sawtooth pattern with sharp zero-crossings at these same points. These results establish distinct transport fingerprints for the two systems in the extreme quantum limit, and provide a theoretical framework for interpreting magnetotransport experiments on GNRs.
ER -