The interactions between acceptors in semiconductors are often treated in
qualitatively the same manner as those between donors. Acceptor wave functions
are taken to be approximately hydrogenic and the standard hydrogen molecule
Heitler-London model is used to describe acceptor-acceptor interactions. But
due to valence band degeneracy and spin-orbit coupling, acceptor states can be
far more complex than those of hydrogen atoms, which brings into question the
validity of this approximation. To address this issue, we develop an
acceptor-acceptor Heitler-London model using single-acceptor wave functions of
the form proposed by Baldereschi and Lipari, which more accurately capture the
physics of the acceptor states. We calculate the resulting acceptor-pair energy
levels and find, in contrast to the two-level singlet-triplet splitting of the
hydrogen molecule, a rich ten-level energy spectrum. Our results, computed as a
function of inter-acceptor distance and spin-orbit coupling strength, suggest
that acceptor-acceptor interactions can be qualitatively different from
donor-donor interactions, and should therefore be relevant to the control of
two-qubit interactions in acceptor-based qubit implementations, as well as the
magnetic properties of a variety of p-doped semiconductor systems. Further
insight is drawn by fitting numerical results to closed-form energy-level
expressions obtained via an acceptor-acceptor Hubbard model.Comment: 19 pages, 10 figures, text revised, figure quality improved,
additional references adde
