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

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.

Figures (5)

• Figure 1: Partition function $Z$ of the gauge-invariant deformed graphene as a function of $\tau$ for different values of $\bar{\Theta}$ and $\bar{\eta}$.
• Figure 2: Reduced thermal quantities of the gauge-invariant deformed graphene, namely $\overline{F}$, $\overline{U}$, $\overline{S}$, and $\overline{C}$, as functions of $\tau$ for different values of $\bar{\Theta}$ and $\bar{\eta}$.
• Figure 3: Partition function $Z$ of the gauge-invariant deformed graphene vs. $\bar{\Theta}$ and $\bar{\eta}$ for different values of $\tau$.
• Figure 4: Reduced thermal quantities of the gauge-invariant deformed graphene, namely $\overline{F}$, $\overline{U}$, $\overline{S}$, and $\overline{C}$, vs. $\bar{\Theta}$ and $\bar{\eta}$ for different values of $\tau$.
• Figure 5: (a) Comparison of partition functions $Z_{1}$ (Hurwitz) and $Z_{2}$ (Euler--Maclaurin); (b) Log-Scale deviation between Euler--Maclaurin and Hurwitz results Vs. $\tau$, for commutative and NC cases.