Spin-orbit and electronic interactions in narrow-gap quantum dots

Abstract

We present a detailed analysis of spin-orbit couplings in zinc-blende narrow-gap parabolic quantum dots built in the plane of a two-dimensional electron gas. Such couplings are related to both bulk (Dresselhaus) and surface (Rashba) inversion asymmetry terms in the Hamiltonian of the system. We start by focusing on how the pure Fock-Darwin spectrum of an InSb quantum dot is modified by the addition of separate terms of spin-orbit coupling; we then deal with the presence of all spin-orbit terms in the numerical diagonalization of the single-particle model. We also consider a two-electron quantum dot---by antisymmetrizing the one-electron basis---and study the competition between electron-electron and spin-orbit interactions. All these effects are analyzed in the presence of a magnetic field perpendicular to the quantum dot. Selection rules for spin-orbit-induced level anticrossings, as well as critical fields and energy minigaps related to them, zero-field energy splittings, and the role of the $g$-factor on the spectrum are also addressed.