Microscopic origin of optical nonlinearities associated with excitations between valence minibands in p-type GaAs-AlAs and Si-${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ heterostructures

We have carried out full-scale semiempirical relativistic pseduopotential calculations of the frequency dependence—spanning the midinfrared to far infrared range of frequencies—of ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$(-2ω;ω,ω) associated with excitations between valence minibands in p-type GaAs-AlAs and Si-SiGe heterostructures. We find that the spectrum is dominated by excitations lying further from the center of the Brillouin zone and depends on states lying above the semiclassical barrier.