ADIABATIC AND ONE-SUBBAND APPROXIMATIONS TO DESCRIBE HOLE BOUND-STATES IN SPHERICAL POTENTIALS FOR CUBIC SEMICONDUCTORS

An adiabatic approximation is suggested for the description of the hol e bound states in spherical potentials for cubic semiconductors. This approximation is based on the separation of the hole motion into a fas t part related to the hole spin and a slow part related to the hole mo mentum. The ratio of frequencies of these two aspects of the hole moti on is given approximately by the ratio M(h)/m(l), where M(h) and m(l) are the masses of the heavy and light holes. An exact solution of the adiabatic Schrodinger equation has been found for the case of a spheri cal harmonic oscillator and a good analytical approximation has been o btained for the four lowest levels in the Coulomb potential. For the-d escription of the upper bound states, the one-subband approximation is suggested. The characteristic feature of this approximation is the ap pearance of an additional gauge vector field with a magnetic monopolel ike structure, which affects the hole motion in momentum space. This f ield is a result of the Berry geometric phase, which originates from t he rigid connection between spin and momentum of a hole. Exact analyti cal solutions of the one-subband Schrodinger equation were found for b oth the spherical harmonic oscillator and the Coulomb potentials. It c an be seen from these solutions that the Berry geometric phase actuall y leads to a noninteger quantization condition for hole bound states.