Thermal Properties of Gauge-Invariant Graphene in Noncommutative Phase-Space

TL;DR

This paper investigates the thermal properties of gauge-invariant graphene in a noncommutative phase-space, deriving analytical expressions for thermodynamic quantities using a gauge-invariant Hamiltonian and ladder-operator formalism.

Contribution

It introduces a gauge-invariant noncommutative Hamiltonian for graphene in a magnetic field and analyzes its thermal properties through analytical and numerical methods.

Findings

Deformed Landau levels and eigenstates due to noncommutativity

Analytical expressions for thermodynamic quantities

Numerical evaluation of thermal properties

Abstract

We study graphene in an external magnetic field within a noncommutative (NC) framework. A gauge-invariant NC Hamiltonian is derived, and the system is analyzed using the ladder-operator formalism, yielding deformed Landau levels and eigenstates. The thermal properties of gauge-invariant NC graphene are then investigated via the partition function, constructed using Euler and Hurwitz zeta functions. Analytical expressions for the partition function, free energy, internal energy, entropy, and specific heat are obtained and numerically evaluated.