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We present a full derivation of the interaction Hamiltonian for holes insilicon within the six-band envelope-function scheme, which appropriatelydescribes the valence band close to the $\boldsymbol{\Gamma}$ point. The fullstructure of the single-hole eigenstates is taken into account, including theBloch part. The scattering processes caused by the Coulomb interaction areshown to be both intraband and interband, the latter being mostly short-ranged.In the asymptotic long-range limit, the effective potential tends to thescreened Coulomb potential, and becomes purely intraband, as assumed inprevious models. We apply our model to compute the excitation spectra of twointeracting holes in prototypical silicon quantum dots, taking into accountdifferent dielectric environments. It is shown that, in the highly screenedregime, short-range interactions (both intra- and inter-band) can be veryrelevant, while they lose importance when there is no screening other than theone proper of the bulk silicon crystal. In the latter case, we predict theformation of hole Wigner molecules.

Inter- and intra-band Coulomb interactions between holes in silicon nanostructures