Self-consistent electronic structure of parabolic semiconductor quantum wells: Inhomogeneous-effective-mass and magnetic-field effects

We report the results of self-consistent density-functional electronic-structure calculations for parabolic-profile GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells in a magnetic field within the effective-mass approximation. We discuss in general the treatment of inhomogeneous effective mass in self-consistent electronic-structure calculations and, in particular, include the parabolic-well effective-mass variation across the well. We consider both in-plane and transverse-magnetic field. In the former case, the magnetic field couples the in-plane and transverse degrees of freedom. We demonstrate that the inhomogeneous effective mass causes a similar coupling that has not previously been taken correctly into account even in the case of simple heterojunctions. We numerically solve the coupled equations self-consistently with Poisson’s equation, including the effects of exchange and correlation in the local-density approximation. We present samples of our results for density profiles, wave functions, and Fermi-level and subband energy dispersions as a function of electron-integrated sheet density ${\mathit{N}}_{\mathit{s}}$ and magnetic field.