Yt. Rebane, ADIABATIC AND ONE-SUBBAND APPROXIMATIONS TO DESCRIBE HOLE BOUND-STATES IN SPHERICAL POTENTIALS FOR CUBIC SEMICONDUCTORS, Physical review. B, Condensed matter, 48(16), 1993, pp. 11772-11781
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.