Effect of coexistence of random potential and electron-electron interaction in two-dimensional systems: Wigner glass

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Abstract
A numerical study of two-dimensional electron systems in strong magnetic fields in the presence of both random potential and electron-electron interaction is performed. The interplay of randomness and many-body effects in this quantum system is investigated by varying the relative strength of random potential and Coulcomb interaction. The electron-electron interaction is treated in the self-consistent Hartree-Fock approximation. The formalism covers arbitrary value of the relative strength of random potential and Coulomb interaction, and the results exhibit behaviour ranging from the Wigner crystallisation or the charge density wave with strong Coulomb interaction to the previously reported Anderson localisation with dominant random potential. It is shown that, in the general case when both random potential and electron-electron interaction are present with comparable magnitudes, the ground state of the system consists of an amorphous array of charge density maxima, which may be called a 'Wigner glass' or a 'charge density glass'. A discussion is made of the behaviour of the charge density in the ground state and its dependence on the occupancy of a Landau sub-band.