Thermodynamic properties of a magnetically modulated graphene

TL;DR

This paper investigates how magnetic modulation affects the thermodynamic properties of graphene under a magnetic field, revealing oscillations and phase differences compared to electric modulation and 2DEG, with explicit formulas provided.

Contribution

It provides a detailed analysis of magnetic modulation effects on graphene's thermodynamics, including oscillation behavior and phase differences, with explicit asymptotic expressions.

Findings

Weiss-type and de Haas-van Alphen oscillations observed at different magnetic field regimes.

Phase difference in oscillations between magnetic and electric modulations in graphene.

Explicit asymptotic formulas for density of states and Helmholtz free energy.

Abstract

The effect of magnetic modulation on thermodynamic properties of a graphene monolayer in presence of a constant perpendicular magnetic field is reported here. One-dimensional spatial electric or magnetic modulation lifts the degeneracy of the Landau levels and converts into bands and their band width oscillates with magnetic field leading to Weiss-type oscillation in the thermodynamic properties. The effect of magnetic modulation on thermodynamic properties of a graphene sheet is studied and then compared with electrically modulated graphene and magnetically modulated conventional two-dimensional electron gas (2DEG). We observe Weiss-type and de Haas-van Alphen (dHvA) oscillations at low and high magnetic field, respectively. There is a definite phase difference in Weiss-type oscillations in thermodynamic quantities of magnetically modulated graphene in compare to electrically modulated graphene. On the other hand, the phase remains same and amplitude of the oscillation is large when compared with the magnetically modulated 2DEG. Explicit asymptotic expressions of density of states and the Helmholtz free energy are provided to understand the phase and amplitude of the Weiss-type oscillations qualitatively. We also study thermodynamic properties when both electric and magnetic modulations are present. The Weiss-type oscillations still exist when the modulations are out-of-phase.