Wigner Crystallization of a two dimensional electron gas in a magnetic field: single electrons versus electron pairs at the lattice sites

摘要

The ground state energy and the lowest excitations of a two dimensionalWigner crystal in a perpendicular magnetic field with one and two electrons percell is investigated. In case of two electrons per lattice site, theinteraction of the electrons {\em within} each cell is taken into accountexactly (including exchange and correlation effects), and the interaction {\embetween} the cells is in second order (dipole) van der Waals approximation. Nofurther approximations are made, in particular Landau level mixing and {\emin}complete spin polarization are accounted for. Therefore, our calculationcomprises a, roughly speaking, complementary description of the bubble phase(in the special case of one and two electrons per bubble), which was proposedby Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation.The phase diagram shows that in GaAs the paired phase is energetically morefavorable than the single electron phase for, roughly speaking, filling factor$f$ larger than 0.3 and density parameter $r_s$ smaller than 19 effective Bohrradii (for a more precise statement see Fig.s 4 and 5). If we start within thepaired phase and increase magnetic field or decrease density, the pairs firstundergo some singlet- triplet transitions before they break.