  In the envelope-function approximation, interband transitions produced by
electric fields are neglected. However, electric fields may lead to a spatially
local ($k$-independent) coupling of band (internal, pseudospin) degrees of
freedom. Such a coupling exists between heavy-hole and light-hole (pseudo-)spin
states for holes in III-V semiconductors, such as GaAs, or in group IV
semiconductors (germanium, silicon, ...) with broken inversion symmetry. Here,
we calculate the electric-dipole (pseudospin-electric) coupling for holes in
GaAs from first principles. We find a transition dipole of $0.5$ debye, a
significant fraction of that for the hydrogen-atom $1s\to2p$ transition. In
addition, we derive the Dresselhaus spin-orbit coupling that is generated by
this transition dipole for heavy holes in a triangular quantum well. A
quantitative microscopic description of this pseudospin-electric coupling may
be important for understanding the origin of spin splitting in quantum wells,
spin coherence/relaxation ($T_2^*/T_1$) times, spin-electric coupling for
cavity-QED, electric-dipole spin resonance, and spin non-conserving tunneling
in double quantum dot systems.
