Broken-Symmetry States of Dirac Fermions in Graphene with A Partially Filled High Landau Level

TL;DR

This study numerically investigates the behavior of Dirac fermions in graphene's N=3 Landau level, revealing a charge density wave instability and stripe phase formation at half-filling, which are experimentally observable and depend on system size.

Contribution

It provides the first numerical evidence of stripe and bubble phases in the N=3 Landau level of graphene, highlighting their stability and experimental relevance.

Findings

Charge density wave peaks grow with system size

Stripe phase forms at large system size

Quantum phases are observable via transport measurements

Abstract

We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wavevectors $\pm {\bf q^{*}}$. Finite-size scaling shows that the peak value grows with electron number and diverges in the thermodynamic limit, which suggests an instability toward a charge density wave. A symmetry broken stripe phase is formed at large system size limit, which is robust against purturbation from disorder scattering. Such a quantum phase is experimentally observable through transport measurements. Associated with the special wavefunctions of the Dirac LL, both stripe and bubble phases become possible candidates for the ground state of the Dirac fermions in graphene with lower filling factors in the N=3 LL.