Quantum critical scaling in magnetic field near the Dirac point in graphene

TL;DR

This paper investigates the scaling behavior of interaction-induced energy gaps near the Dirac point in graphene under magnetic fields, revealing universal functions and sublinear gap dependence consistent with experiments.

Contribution

It provides an exact computation of universal scaling functions for Landau level gaps in graphene with many Dirac fermions, highlighting a sublinear magnetic field dependence.

Findings

Universal scaling functions are computed exactly.

The gap at f=1 is bounded by E(1)/C.

Results agree quantitatively with experimental observations.

Abstract

Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor f=1 in graphene we discuss the scaling of the interaction-induced gaps in vicinity of the Dirac point with the magnetic field. The gap at f=1 is shown to be bounded from above by E(1)/C, where E(n) are the Landau level energies and C = 5.985 + O(1/N) is a universal number. The universal scaling functions are computed exactly for a large number of Dirac fermions N. We find a sublinear dependence of the gap at the laboratory magnetic fields for realistic values of short-range repulsion between electrons, and in quantitative agreement with observation.