Integer Quantum Hall Effect in Graphene

We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges effect as a pseudo-potential varying continuously along the $x$ direction. At low temperature and in the weak electric field limit, we explicitly determine the thermodynamical potential. With this, we derive the particle numbers in terms of the quantized flux and therefore the Hall conductivity immediately follows.