First-principles envelope-function theory for lattice-matched semiconductor heterostructures

Abstract

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent heterostructures with macroscopically neutral interfaces and no spontaneous bulk polarization. The key assumption -- proved in earlier numerical studies -- is that the heterostructure can be treated as a weak perturbation with respect to some periodic reference crystal, with the nonlinear response small in comparison to the linear response. Quadratic response theory is then used in conjunction with k.p perturbation theory to develop a multi-band effective-mass Hamiltonian (for slowly varying envelope functions) in which all interface band-mixing effects are determined by the linear response. To within terms of the same order as the position dependence of the effective mass, the quadratic response contributes only a bulk band offset term and an interface dipole term, both of which are diagonal in the effective-mass Hamiltonian. Long-range multipole Coulomb fields arise in quantum wires or dots, but have no qualitative effect in two-dimensional systems beyond a dipole contribution to the band offsets.

25 pages, no figures, RevTeX4; v3: final published version

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• Interface Contributions to the Spin-Orbit Interaction Parameters of Electrons at the (001) GaAs/AlGaAs Interface
• Valence-band mixing in first-principles envelope-function theory
• Current-induced Spin Polarization in Two-Dimensional Hole Gas
• Spin splitting of two dimensional states in the conduction band of asymmetric heterostructures: contribution from the atomically sharp interface
• Least action principle for envelope functions in abrupt heterostructures
• Theory of electrons, holes and excitons in GaAs polytype quantum dots
• Multiscale theory of valley splitting
• Accurate quadratic-response approximation for the self-consistent pseudopotential of semiconductor nanostructures
• Quadratic response theory for spin-orbit coupling in semiconductor heterostructures
• First-principles effective-mass Hamiltonian for semiconductor nanostructures in a magnetic field
• Interface states in two-dimensional electron systems with spin-orbital interaction