Quadrupolar interactions between acceptor pairs in p-doped semiconductors

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.

arXiv comment12 pages, 6 figures, as published in PRB

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Cited by in corpus (5)

• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• A linear combination of atomic orbitals (LCAO) model for deterministically placed acceptor arrays in silicon
• Hole in one: Pathways to deterministic single-acceptor incorporation in Si(100)-2$\times$1
• Multi-hole models for deterministically placed acceptor arrays in silicon
• Tug-the-hook symmetry for quantum 6j-symbols