Enhanced plasmon anomaly in the dynamical conductivity of heterostructures with large spacer

We calculate the frequency-dependent scattering rate M’ ’(ω), which determines the dynamical conductivity of a disordered two-dimensional electron gas. The existence of plasmons in an interacting electron gas gives rise to a strongly frequency-dependent scattering rate. For ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs heterostructures with large spacer width α, we get an analytical result for the scattering rate: M’ ’(ω)=M’ ’(0)[1+A‖ω${\mathrm{\Vert }}^5$Rexp(-B${\mathrm{\omega }}^2$)]. The coefficients A and B depend on the Fermi wave number $k_F$, the effective Bohr radius $a^{\mathrm{*}}$, and α. $M prime prime ( omega )— peaks at ${\mathrm{\omega }}_0$=${\mathrm{\varepsilon }}_{\mathit{F}}$(5${\mathit{a}}^{\mathrm{*}}$/α${)}^{1/2}$/(${\mathit{k}}_{\mathit{F}}$ ${\mathrm{a}}^{\mathrm{*}}$), where ${\varepsilon }_F$ is the Fermi energy. The high-frequency scattering rate is also calculated: M’ ’(ω≫2${\varepsilon }_F$)≪M’ ’(0). We predict a maximum linewidth for plasmons with wave number $q_0$=5/(4α). The relevance of our theory to anomalies found in cyclotron-resonance experiments is discussed.