Effective Action and Mean Fermion Number Density of Graphene in Constant Magnetic Field at Finite Temperature and Density

TL;DR

This paper calculates the effective action and mean fermion number density of graphene under a magnetic field at finite temperature and density, revealing a temperature-dependent fermion condensation phenomenon.

Contribution

It provides closed-form expressions for these quantities and explores their temperature dependence, extending understanding of graphene's quantum behavior under external fields.

Findings

Mean fermion number density peaks at a specific temperature

Fermion condensation occurs in graphene at low temperatures

Results suggest temperature-dependent quantum phase behavior

Abstract

The effective action and the mean fermion number density of graphene in constant external magnetic field at finite temperature and density are calculated. Closed expressions for these are given and their variation with temperature are studied. It is found that the mean fermion number density peaks around a particular temperature, depending on the chemical potential at low temperatures. This feature is interpreted as 'condensation of fermions ${\bar{\psi}}{\psi}$' in graphene. In future, it is interesting to extend and explore this calculation and the work of the reference [20] for the case of Graphyne [23].