Self-consistent density of states for a single- and double-quantum-well structure in a parallel magnetic field

The electron energy eigenstates for an isolated and a pair of strongly coupled quantum-well structures with a quantizing magnetic field ${\mathit{B}}_{\mathrm{|}\mathrm{|}}$ parallel to the planes are calculated. Numerical results are presented for the energy eigenvalues as a function of ${\mathit{B}}_{\mathrm{|}\mathrm{|}}$ as well as the in-plane wave number ${\mathit{k}}_{\mathit{y}}$. The results show a crossover behavior as the magnetic field is increased, with the critical magnetic field corresponding to the well width being equal to the magnetic length. This implies that for the pair of coupled quantum wells the tunneling between wells is suppressed in the high magnetic field regime with the electrons confined to the wells, which is also evident from the wave functions. In the low magnetic field regime, the energy eigenvalue spectrum is more densely distributed compared to the high magnetic field region. When plotted as a function of ${\mathit{k}}_{\mathit{y}}$, the energy spectra for both the single- and double-quantum-well systems have gaps. The eigenfunctions for the lowest states are also presented for ${\mathit{k}}_{\mathit{y}}$=0 and ${\mathit{k}}_{\mathit{y}}$ finite to demonstrate their dependence on this wave vector. These results are used to obtain the partial density of states for each energy eigenvalue as a function of the electron energy for fixed magnetic field strength. The role played by impurity scattering is included in the self-energy, through the self-consistent Born approximation. The magnitude of the contribution from the self-energy to the partial density of states increases with the magnetic field. The role played by the electron tunneling between coupled wells for the self-consistent density of states is included. © 1996 The American Physical Society.