Tunneling density of states and plasmon excitations in double-quantum-well systems

We calculate the tunneling density of states and plasmon excitations in a double-quantum-well system. In these calculations, the barriers are doped uniformly. The eigenfunctions are first obtained in the Hartree approximation and these results are then used to calculate the exchange contribution in lowest order. This is a simple way to include the effects due to temperature on the intersubband transition energies. We present a self-consistent-field theory and numerical calculations for the intersubband plasmon excitation energies. The derived analytical results show that in the long wavelength limit the symmetric mode is not affected by tunneling but the antisymmetric mode depends on the charge transfer between the quantum wells. The results for the antisymmetric modes include corrections to previous results where tunneling between the layers was neglected. For the symmetric mode, the sign of the charge density fluctuations in each quantum well is the same and the double-well structure is completely symmetric with respect to the midplane. There is a preferred direction for electrons to tunnel when the charge density fluctuations in the wells have opposite signs which cause the plasmon frequency for the antisymmetric case to depend on tunneling. We also show that in the quasiclassical regime (q≪${\mathit{k}}_{\mathrm{TF}}$) there is no minimum separation between the charged layers for the plasmon excitations with wave number q not to be Landau damped. We also examine the effect on the tunneling density of states and the plasmon excitation spectrum when the doping density of the barriers is not the same; specifically, the volume dopant density in the left barrier is larger than the dopant density in the other two barriers, which are assumed to be equally doped.