The inelastic relaxation time due to electron-electron collisions in high-mobility two-dimensional systems under microwave radiations

In some theoretical analyses of microwave-induced magnetoresistance oscillations in high-mobility two-dimensional systems, the "inelastic relaxation time" $\tau_{in}$ due to electron-electron scattering is evaluated using an equilibrium distribution function $f^0$ in the absence of radiation, and it is concluded that $\tau_{in}$ is much larger than $\tau_{q}$, the single-particle relaxation time due to impurity scattering. However, under the irradiation of a microwave capable of producing magnetoresistance oscillation, the distribution function of the high-mobility electron gas deviates remarkably from $f^0$ at low temperatures. Estimating $\tau_{in}$ using an approximate nonequilibrium distribution function rather than using $f^0$, one will find the system to be in the opposite limit $1/\tau_{in}\ll 1/\tau_{q}$ even for T=0 K. Therefore, models which depend on the assumption $1/\tau_{in}\gg 1/\tau_{q}$ may not be justifiable.