Nonequilibrium phase transitions in a quasi-two-dimensional superlattice   with parabolic miniband
  Distribution function and current density in a one-dimensional superlattice with parabolic miniband are calculated. The current dependence on the temperature coincides with experimental data. Generalization is carried out to quasi-two-dimensional superlattice with paraboloidal miniband. For a sample opened in Y direction with dc current in X direction, a novel nonequilibrium phase transition is found, namely, appearing a spontaneous transverse electric field under temperature rising. 
G. M. Shmelev, T. A. Gorshenina, E. M. Epshtein