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arXiv · 1601.07130

Electron-solid and electron-liquid phases in graphene

M. E. Knoester·Z. Papic·C. Morais Smith
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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.

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M. E. Knoester, Z. Papic, C. Morais Smith. 2016-01-26. Electron-solid and electron-liquid phases in graphene. https://doi.org/10.1103/physrevb.93.155141

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