  Spintronics, quantum computing and quantum communication science utilizing
cubic semiconductors rely largely on the properties of the hole states,
composed of light and heavy hole wavefunction components. The admixture of
light-hole (LH) into ground hole state predominately by the heavy hole (HH)
would induce unique features of LH in optical transitions, spin relaxation, and
spin polarization. We point to an unexpected source of HH-LH mixing in quantum
dots, arguing that in contrast with current models the mixing does not reflect
the strain between the dot and its matrix and does not scale inversely with the
energy splitting between the bulk HH and LH states. Instead, we show via
atomistic pseudopotential calculations on a range of strained and unstrained
dots of different symmetries that the HH-LH mixing is enabled by the presence
in the QD of a dense ladder of intermediate states between the HH and LH states
which amplifies and propagates this interaction and leads to "supercoupling"
(analogous to super-exchange in magnetism). This explains a number of
outstanding puzzles regarding the surprising large coupling seen in unstrained
QD (GaAs/AlAs) of ideal shapes and the surprising fact that in strained QD
(InAs/GaAs) the coupling is very strong despite the fact that the 12-fold
increase in bulk HH-LH splitting overrides the ~4 fold enhancement of the
coupling matrix element by strain in comparison with unstrained GaAs QDs.
