Temperature-dependent compressibility in graphene and two-dimensional systems

TL;DR

This paper investigates how the electronic compressibility of graphene and 2D semiconductor systems varies with temperature, revealing non-monotonic behavior influenced by exchange interactions and kinetic energy effects.

Contribution

It provides the first detailed analysis of temperature-dependent compressibility in monolayer and bilayer graphene within the Hartree-Fock approximation, highlighting non-monotonic trends and specific temperature corrections.

Findings

2D systems show inverse compressibility decreasing then increasing with temperature.

Monolayer graphene's inverse compressibility always remains positive and varies oppositely.

At high temperatures, bilayer graphene's inverse compressibility approaches a smaller constant.

Abstract

We calculate the finite temperature compressibility for two-dimensional semiconductor systems, monolayer graphene, and bilayer graphene within the Hartree-Fock approximation. We find that the calculated temperature dependent compressibility including exchange energy is non-monotonic. In 2D systems at low temperatures the inverse compressibility decreases first with increasing temperature, but after reaching a minimum it increases as temperature is raised further. At high enough temperatures the negative compressibility of low density systems induced by the exchange energy becomes positive due to the dominance of the finite temperature kinetic energy. The inverse compressibility in monolayer graphene is always positive and its temperature dependence appears to be reverse of the 2D semiconductor systems, i.e., it increases first with temperature and then decreases at high temperatures. The inverse compressibility of bilayer graphene shows the same non-monotonic behavior as ordinary 2D systems, but at high temperatures it approaches a constant which is smaller than the value of the non-interacting bilayer graphene. We find the leading order temperature correction to the compressibility within Hartree-Fock approximation to be $T^2 \ln T$ at low temperatures for all three systems.