Spin and valley Hall effects induced by asymmetric interparticle scattering

We develop the theory of the spin and valley Hall effects in two-dimensional systems caused by asymmetricskew-scattering of the quasiparticles. The collision integral is derived in the third order in the particle-particle interaction with the spin-orbit coupling taken into account both for bosons and for fermions. It is shown that the scattering asymmetry appears only in the processes where interaction between particles in the initial and intermediate states is present. We show that for degenerate electrons or nondegenerate particles the spin and valley currents induced by interparticle collisions are suppressed with their steady-state values being proportional to the squared temperature or density, respectively. Our results imply non-Fermi-liquid properties of electrons in the presence of electron-electron skew scattering. Strong deviations from the conventional picture of interparticle scattering are also demonstrated for the skew scattering of two-dimensional degenerate bosons, e.g., excitons or exciton polaritons: The spin or valley current of degenerate bosons contains the enhancement factor exponentially growing with increase in the particle density.

Automated summary

We develop a theory for the spin and valley Hall effects in two-dimensional systems caused by asymmetricskew-scattering. The results show that the scattering asymmetry only appears in processes where interaction between particles in the initial and intermediate states is present. For degenerate electrons or nondegenerate particles, the spin and valley currents induced by interparticle collisions are suppressed, and their steady-state values are proportional to the squared temperature or density, respectively. The study also demonstrates strong deviations from the conventional picture of interparticle scattering for the skew scattering of two-dimensional degenerate bosons, such as excitons or exciton polaritons.