Heitler-London model for acceptor-acceptor interactions in doped semiconductors

Durst, Adam C.; Castoria, Kyle E.; Bhatt, R. N.

doi:10.1103/physrevb.96.155208

Cited by 5 publications

(8 citation statements)

References 67 publications

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“…The interactions between a pair of acceptors in the spherical model have been studied by Durst, et. al., in the framework of a Heitler-London model 10 ; later, they found that the inter-acceptor interactions in the same model are dominated at large distance by electric quadrupole moments 11 . For linear chains of acceptors, an independent-hole model was developed, including the contribution of cubic terms, and the existence of nontrivial single-particle topological edge states was demonstrated for finite chains, and related to band invariants of the corresponding infinite systems 12 .…”

Section: Introductionmentioning

confidence: 98%

Linear combination of atomic orbitals model for deterministically placed acceptor arrays in silicon

Zhu

Fisher

2020

Phys. Rev. B

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We develop a tight-binding model based on linear combination of atomic orbitals (LCAO) methods to describe the electronic structure of arrays of acceptors, where the underlying basis states are derived from an effective-mass-theory solution for a single acceptor in either the spherical approximation or the cubic model. Our model allows for arbitrarily strong spin-orbit coupling in the valence band of the semiconductor. We have studied pairs and dimerised linear chains of acceptors in silicon in the 'independent-hole' approximation, and investigated the conditions for the existence of topological edge states in the chains. For the finite chain we find a complex interplay between electrostatic effects and the dimerisation, with the long-range Coulomb attraction of the hole to the acceptors splitting off states localised at the end acceptors from the rest of the chain. A further pair of states then splits off from each band, to form a pair localised on the next-to-end acceptors, for one sense of the bond alternation and merges into the bulk bands for the other sense of the alternation. We confirm the topologically non-trivial nature of these next-to-end localised states by calculating the Zak phase. We argue that for the more physically accessible case of one hole per acceptor these long-range electrostatic effects will be screened out; we show this by treating a simple phenomenologically screened model in which electrostatic contributions from beyond the nearest neighbours of acceptor each pair are removed. Topological states are now found on the end acceptors of the chains. In some cases the termination of the chain required to produce topological states is not the one expected on the basis of simple geometry (short versus long bonds); we argue this is because of a non-monotonic relationship between the bond length and the effective Hamiltonian matrix elements between the acceptors.

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Section: Introductionmentioning

confidence: 98%

Linear combination of atomic orbitals model for deterministically placed acceptor arrays in silicon

Zhu

Fisher

2020

Phys. Rev. B

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“…It is an eight-level spectrum [see Eq. (27)] controlled by a single interaction parameter, J(R, µ) = Q 0 (µ) 2 /R 5 , where the seven excited-state energy levels are separated from the ground state by 3J, 5J, 7J, 8J, 10J, 13J, and 15J, respectively. From low energy to high, the degeneracy of these eight levels is 2, 2, 3, 1, 2, 4, 1, and 1.…”

Section: Discussionmentioning

confidence: 99%

“…The details of this procedure are provided in Appendix B of Ref. 27. The resulting radial functions are plotted in Fig.…”

Section: A Single Acceptor Modelmentioning

confidence: 99%

“…In prior work 27 , we used the Baldereschi-Lipari singleacceptor wave functions to develop a Heitler-London model for the acceptor pair. This numerical calculation provided the acceptor-pair energy spectrum for input values of material parameters and inter-acceptor separation, but due to computational constraints, its results were limited to acceptors separated by less than a few effective Bohr radii.…”

Section: Introductionmentioning

confidence: 99%

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Quadrupolar interactions between acceptor pairs in p -doped semiconductors

2020

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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 can be traced to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-j symbol, 2 2 2 3 2 3 2 3 2 = 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 p-type semiconductors.

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“…The electronic structure of a single acceptor can most simply be described by the "spherical model" [6][7][8][9], which includes spin-orbit coupling but neglects the cubic anisotropy of the host semiconductor and offers reasonable results for the electronic structure of an isolated acceptor. The interactions between a pair of acceptors in the spherical model have been studied by Durst et al in the framework of a Heitler-London model [10]; later, they found that the interacceptor interactions in the same model are dominated at large distance by electric quadrupole moments [11]. For linear chains of acceptors, an independent-hole model was developed, including the contribution of cubic terms, and the existence of nontrivial single-particle topological edge states was demonstrated for finite chains, and related to band invariants of the corresponding infinite systems [12].…”

Section: Introductionmentioning

confidence: 99%

Multihole models for deterministically placed acceptor arrays in silicon

Zhu

Fisher

2021

Phys. Rev. B

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In this paper, we compute the electronic structure of acceptor clusters in silicon by using three different methods to take into account electron correlations: the full configuration interaction (full CI calculation), the Heitler-London approximation (HL approximation), and the unrestricted Hartree-Fock method (UHF method). We show that both the HL approach and the UHF method are good approximations to the ground state of the full CI calculation for a pair of acceptors and for finite linear chains along [001], [110], and [111]. The total energies for finite linear chains show the formation of a fourfold-degenerate ground state (lying highest in energy), below which there are characteristic low-lying eightfold and fourfold degeneracies, when there is a long (weak) bond at the end of the chain. We present evidence that this is a manifold of topological edge states. We identify a change in the angular momentum composition of the ground state at a critical pattern of bond lengths, and show that it is related to a crossing in the Fock matrix eigenvalues. We also test the symmetry of the self-consistent mean-field UHF solution and compare it to the full CI; the symmetry is broken under almost all the arrangements by the formation of a magnetic state in UHF, and we find further broken symmetries for some particular arrangements related to crossings (or potential crossings) between the Fock-matrix eigenvalues in the [001] direction. We also compute the charge distributions across the acceptors obtained from the eigenvectors of the Fock matrix; we find that, with weak bonds at the chain ends, two holes are localized at either end of the chain while the others have a nearly uniform distribution over the middle; this also implies the existence of the nontrivial edge states. We also apply the UHF method to treat an infinite linear chain with periodic boundary conditions, where the full CI calculation and the HL approximation cannot easily be used. We find the band structures in the UHF approximation, and compute the Zak phases for the occupied Fock-matrix eigenvalues; however, we find they do not correctly predict the topological edge states formed in this interacting system. On the other hand, we find that direct study of the quantum numbers characterizing the edge states, introduced by Turner et al. [Phys. Rev. B 83, 075102 (2011)], provides a better insight into their topological nature.

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Heitler-London model for acceptor-acceptor interactions in doped semiconductors

Cited by 5 publications

References 67 publications

Linear combination of atomic orbitals model for deterministically placed acceptor arrays in silicon

Linear combination of atomic orbitals model for deterministically placed acceptor arrays in silicon

Quadrupolar interactions between acceptor pairs in p -doped semiconductors

Multihole models for deterministically placed acceptor arrays in silicon

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