Quadrupolar interactions between acceptor pairs in $$\mathcal{p}$$-doped semiconductors

Journal Article · 21 January 2020 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.101.035202 · OSTI ID:1801538

Durst, Adam C.  ^[1]; Yang-Mejia, Genesis  ^[2]; Bhatt, R. N. ^[3]

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1. Hofstra University, Hempstead, NY (United States); OSTI
2. Hofstra University, Hempstead, NY (United States)
3. Princeton Univ., NJ (United States); Institute for Advanced Study, Princeton, NJ (United States)

Here, we consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor 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-$$\mathcal{j}$$ symbol, $$^\{\frac{^2_3}{\small2} \frac{^2_3}{\small2} \frac{^2_3}{\small2}$$$$^\}$$ = 0. 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 $$\mathcal{p}$$-type semiconductors.

• Research Organization: Princeton Univ., NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0002140
• OSTI ID: 1801538
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 101; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English