Electron-solid and electron-liquid phases in graphene

TL;DR

This paper analyzes the competition between electron-solid and liquid phases in graphene's Landau levels, highlighting how wave function differences influence phase stability and providing analytical and numerical energy calculations.

Contribution

It introduces a detailed comparison of electron-solid and liquid phases in graphene, accounting for relativistic effects via a form factor and computing energies with new analytical and numerical methods.

Findings

Liquid phase dominates in the n=1 Landau level.

Electron-solid phases are more prominent in higher Landau levels (n=2, 3).

Wave function differences affect phase energies in graphene.

Abstract

We investigate the competition between electron-solid and quantum-liquid phases in graphene, which arise in partially filled Landau levels. The differences in the wave function describing the electrons in the presence of a perpendicular magnetic field in graphene with respect to the conventional semiconductors, such as GaAs, can be captured in a form factor which carries the Landau level index. This leads to a quantitative difference in the electron-solid and -liquid energies. For the lowest Landau level, there is no difference in the wave function of relativistic and non-relativistic systems. We compute the cohesive energy of the solid phase analytically using a Hartree-Fock Hamiltonian. The liquid energies are computed analytically as well as numerically, using exact diagonalization. We find that the liquid phase dominates in the n=1 Landau level, whereas the Wigner crystal and electron-bubble phases become more prominent in the n=2 and n=3 Landau level.