Cyclotron resonance in two interacting electron systems with application to Si inversion layers

Abstract

We have investigated the cyclotron resonance for two degenerate electron systems interacting with one another through the electron-electron collision time ${\ensuremath{\tau}}_{e}(T)$ defined as the relaxation time of the relative momentum. The coupled kinetic equations for the total and the relative momentum are solved in the presence of a static magnetic field and a frequency-dependent electric field. The solution for the power absorption is discussed in terms of the concentration ratio of the electrons, $\frac{{n}_{1}}{{n}_{2}}$, and the parameters $\frac{{\ensuremath{\tau}}_{1}}{{\ensuremath{\tau}}_{e}}$, $\frac{{\ensuremath{\tau}}_{2}}{{\ensuremath{\tau}}_{e}}$, where ${\ensuremath{\tau}}_{1,2}$ are ordinary scattering times. We find that our results are consistent with the observed temperature dependence of the cyclotron resonance of inversion layer electrons in Si, for $T\ensuremath{\gtrsim}25\ifmmode^\circ\else\textdegree\fi{}$K. At lower temperatures also, the frequency dependence of ${\ensuremath{\tau}}_{e}$ becomes important and affects the cyclotron resonance in a two-electron system, even as $T\ensuremath{\rightarrow}0$.