Dynamics in the quantum Hall effect and the phase diagram of graphene

TL;DR

This paper investigates the mechanisms behind Landau level degeneracy lifting in graphene's quantum Hall effect, revealing coexistence of ferromagnetism and magnetic catalysis, and maps the phase diagram of the system.

Contribution

It provides a detailed analysis of the gap equation solutions in graphene, showing the coexistence of different order parameters and reproducing experimental quantum Hall plateau observations.

Findings

Coexistence of QH ferromagnetism and magnetic catalysis in graphene.

Reproduction of experimentally observed quantum Hall plateaus.

Phase diagram mapping of temperature and chemical potential effects.

Abstract

The dynamics responsible for lifting the degeneracy of the Landau levels in the quantum Hall (QH) effect in graphene is studied by utilizing a low-energy effective model with a contact interaction. A detailed analysis of the solutions of the gap equation for Dirac quasiparticles is performed at both zero and nonzero temperatures. The characteristic feature of the solutions is that the order parameters connected with the QH ferromagnetism and magnetic catalysis scenarios necessarily coexist. The solutions reproduce correctly the experimentally observed novel QH plateaus in graphene in strong magnetic fields. The phase diagram of this system in the plane of temperature and electron chemical potential is analyzed. The phase transitions corresponding to the transitions between different QH plateaus in graphene are described.