Quadrupolar interactions between acceptor pairs in p-doped semiconductors

TL;DR

This paper models acceptor-acceptor interactions in p-doped semiconductors, revealing that quadrupole-quadrupole interactions dominate at large separations and providing universal formulas for their energy spectra.

Contribution

It introduces a simplified, universal model for acceptor pair interactions based on quadrupole moments, applicable to quantum computing and material property calculations.

Findings

Quadrupole moments are nonzero for acceptors, dominating interactions at large distances.

Derived closed-form expressions for energy spectra of acceptor pairs.

Results are material-parameter independent, showing universality.

Abstract

We consider the interaction between acceptor pairs in doped semiconductors in the limit of large inter-acceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, 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. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-j symbol. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating p-type semiconductors.