Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map
arXiv:2509.23763 · doi:10.1140/epjp/s13360-025-06842-8
Abstract
We investigate the relativistic quantum dynamics of amassless electron in graphene in a two-dimensional noncommutative (NC) plane under a constant background magnetic field. To address the issue of gauge invariance, we employ an effective massless NC Dirac field theory, incorporating the Seiberg-Witten (SW) map alongside the Moyal star product. Using this framework, we derive a manifestly gauge-invariant Hamiltonian for a massless Dirac particle, which serves as the basis for studying the relativistic Landau problem in graphene in NC space. Specifically, we analyze the motion of a relativistic electron in monolayer graphene within this background field and compute the energy spectrum of the NC Landau system. The NC-modified energy levels are then used to explore the system's thermodynamic response. Notably, in the low-temperature limit, spatial noncommutativity leads to a spontaneous magnetization-a distinct signature of NC geometry in relativistic condensed matter systems like graphene.
10 pages
References in corpus (8)
- Electric Field Effect in Atomically Thin Carbon Films
- The electronic properties of graphene
- Unconventional Integer Quantum Hall effect in graphene
- Colloquium: The transport properties of graphene: An introduction
- Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
- Turning graphene into a lab for noncommutativity
- Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space
- Density of states and differential entropy in Dirac materials in crossed magnetic and in-plane electric fields