Dissipation due to a ‘‘valley wave’’ channel in the quantum Hall effect of a multivalley semiconductor

When the quantized Hall effect occurs at a semiconductor surface such as Si(110), where the carriers have a time-reversal valley degeneracy, there should be a spontaneous valley polarization at appropriate values of the filling factor ν. There can then be dissipation at T=0 due to radiation of Goldstone bosons (‘‘valley waves’’) at impurity sites, provided that the current density exceeds a critical value ${\mathrm{j}}_{\mathrm{c}}$ determined by the intervalley electron-electron scattering or other terms which modify the valley-wave dispersion at long wavelengths. The dissipation above ${\mathrm{j}}_{\mathrm{c}}$ is described by a constant resistivity ${\mathrm{\rho }}_{\mathrm{xx}}$, which should be small but measureable, and sensitive to the density of neutral impurities.