Full cubic model calculation of quadrupolar interactions between acceptor pairs in p-doped semiconductors including silicon

We consider the interaction between acceptor pairs in doped semiconductors in the limit of large inter-acceptor separation relevant for low doping densities. The dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. In prior work, we modeled single-acceptor ground-state wave functions via the strong-coupling spherical model of Baldereschi and Lipari, calculated the matrix elements of the electric quadrupole tensor between the four degenerate ground states, and used them to construct and diagonalize the quadrupole-quadrupole interaction Hamiltonian. We now improve upon prior results by generalizing to the case of general-coupling cubic-model acceptors, which is particularly important for semiconductors like silicon where valence band spin-orbit splitting is small and cubic terms in the single acceptor Hamiltonian are significant. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as the thermodynamic properties of insulating p-type semiconductors.