Supersymmetry and Correlated Electrons in Graphene Quantum Hall Effect

TL;DR

This paper develops a supersymmetric framework to describe the quantum Hall effect in graphene, revealing how energy levels and degeneracies behave under interactions and magnetic field variations.

Contribution

It introduces a supersymmetric description of graphene's quantum Hall effect, highlighting differences in energy and Landau levels, and explains the emergence of quantum Hall plateaux.

Findings

Supersymmetry applies separately at K and K' points in graphene.

Coulomb interactions induce an excitonic gap at zero energy.

Quantum Hall plateaux occur at specific filling factors depending on magnetic field strength.

Abstract

We present a supersymmetric description of the quantum Hall effect (QHE) in graphene. The noninteracting system is supersymmetric separately at the so-called K and K' points of the Brillouin zone corners. Its essential consequence is that the energy levels and the Landau levels are different objects in graphene QHE. Each energy level has a four-fold degeneracy within the noninteracting theory. With the Coulomb interaction included, an excitonic gap opens in the zero-energy state, while each nonzero energy level splits into two levels since up-spin and down-spin electrons come from different Landau levels. We argue the emergence of the plateaux at $\nu =\pm (4n-2)$ for small magnetic field $B$ and at $\nu =0$, $\pm 1$, $\pm 2n$ for large $B$ with $n$ natural numbers.