Theory of cyclotron resonance lineshape for an electron-impurity system in two dimensions

Using the proper connected diagram expansion which incorporates the quasi-particle effect in a natural manner, we calculated the cyclotron resonance width Γ and frequency shift Δ in the extreme quantum limit, (a) Δ = 0 for any form of interaction potential, (b) Γ ∝ n_I^{$\text{1}\text{2}$}B^{$\text{1}\text{2}$} for a short range interaction, and (c) $\text{Γ = π}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{ze}{}^2\text{k}{}^{\mathrm{?1}}\text{n}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{I}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for the unscreened Coulomb interaction, are obtained in the weak coupling approximation. The result (a) and the field (B)- and concentration (n_I)-dependence in case (b) are in satisfactory agreement with experimental data on the Si space-charge layers at the surface carrier densities higher than 1 × 10¹²cm^-2 and at liquid helium temperatures, where the main source of relaxation is thought to arise from a short-range interaction.