Wigner crystal of a two-dimensional electron gas with a strong spin-orbit interaction

The Wigner-crystal phase of two-dimensional electrons interacting via the Coulomb repulsion and subject to a strong Rashba spin-orbit coupling is investigated. For low enough electronic densities the spin-orbit band splitting can be larger than the zero-point energy of the lattice vibrations. Then the degeneracy of the lower subband results in a spontaneous symmetry breaking of the vibrational ground state. The $60^{\circ}-$rotational symmetry of the triangular (spin-orbit coupling free) structure is lost, and the unit cell of the new lattice contains two electrons. Breaking the rotational symmetry also leads to a (slight) squeezing of the underlying triangular lattice.Comment: 5 pages + appendix, 3 figures, minor improvements to the tex

Transport through molecular junctions with a nonequilibrium phonon population

The calculation of the nonlinear conductance of a single-molecule junction is revisited. The self energy on the junction resulting from the electron-phonon interaction has at low temperatures logarithmic singularities (in the real part) and discontinuities (in the imaginary one) at the frequencies corresponding to the opening of the inelastic channels. These singularities generate discontinuities and logarithmic divergences (as a function of the bias voltage) in the low-temperature differential conductance around the inelastic thresholds. The self energy also depends on the population of the vibrational modes. The case of a vibrating free junction (not coupled to a thermal bath), where the phonon population is determined by the bias voltage is examined. We compare the resulting zero-temperature differential conductance with the one obtained for equilibrated phonons, and find that the difference is larger the larger is the bare transmission of the junction and the product of the electron dwell time on the junction with the phonon frequency.Comment: 4 page