Group theory of electron states in quantum wells and heterostructures

Abstract

A group-theoretical classification of confined electron states in semiconductor quantum wells and heterostructures is presented. It exploits the possible decomposition of an 8×8 k·p Hamiltonian for the conduction-valence band complex into terms of axial, cubic and tetrahedral symmetry. Taking into account only the axial terms, we obtain a unique classification scheme for conduction, valence and split-off subbands and give selection rules for optical intra- and intersubband transitions. These selection rules become relaxed due to the symmetry breaking effect of cubic and tetrahedral terms.