Electron-electron scattering and transport properties of spin-orbit coupled electron gas

We calculate the electrical and thermal conductivity of a two-dimensional electron gas with strong spin--orbit coupling in which the scattering is dominated by electron--electron collisions. Despite the apparent absence of Galilean invariance in the system, the two-particle scattering does not affect the electrical conductivity above the band-crossing point where both helicity bands are filled. Below the band-crossing point where one helicity band is empty, switching on the electron--electron scattering leads only to a limited decrease of the electrical conductivity, so that its high-temperature value is independent of the scattering intensity. In contrast to this, thermal conductivity is not strongly affected by the spin-orbit coupling and exhibits only a kink as the Fermi level passes through the band-crossing point.