Quadrupolar interactions between acceptor pairs in 
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-doped semiconductors

Durst, Adam C.; Yang-Mejia, Genesis; Bhatt, R. N.

doi:10.1103/physrevb.101.035202

Cited by 7 publications

(8 citation statements)

References 54 publications

(70 reference statements)

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“…In the absence of cubic anisotropy, Durst et al 11 argue that the long-range interaction between two acceptors is dominated by quadrupolar effects, which they find favour a doubly degenerate state with total angular momentum M F = ±2 about the core axis. This corresponds to partially aligned pairs of holes, with m F = ±( 3 2 , 1 2 ) on the two acceptors.…”

Section: A a Pair Of Acceptorsmentioning

confidence: 99%

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: A a Pair Of Acceptorsmentioning

confidence: 99%

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

Zhu

Fisher

2020

Phys. Rev. B

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“…We will see that this feature persists in the calculations on larger systems. In the absence of cubic anisotropy, Durst et al [11] argue that the long-range interaction between two acceptors is dominated by quadrupolar effects, which they find favor a doubly degenerate state with total angular momentum M F = ±2 about the core axis. This corresponds to partially aligned pairs of holes, with m F = ±( 32 , 1 2 ) on the two acceptors.…”

Section: A a Pair Of Acceptorsmentioning

confidence: 99%

“…We can also calculate the Zak phase for the occupied UHF states in the infinite system by using (11) in Sec. II A 5.…”

Section: Structure Of the Edge Statesmentioning

confidence: 99%

“…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%

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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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“…These features have led to significant interest in single acceptors in silicon [40][41][42][43][44][45][46], notably finding that with appropriate strain manipulation, long coherence times of ∼10 ms can be achieved [47]. Arrays of such acceptors present possibilities for analog quantum simulation of the extended Fermi-Hubbard model [18], which has motivated several theoretical investigations [48][49][50]. We also note the prospect of ultra doping silicon with acceptors to realize superconductivity, and with that the possibility of fabricating a variety of quantum devices (e.g., wires, Josephson junctions, SQUIDs, etc.)…”

Section: Introductionmentioning

confidence: 99%

Hole in one: Pathways to deterministic single-acceptor incorporation in Si(100)-2$\times$1

Campbell,

Baczewski,

Butera

et al. 2021

Preprint

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Stochastic incorporation kinetics can be a limiting factor in the scalability of semiconductor fabrication technologies using atomic-precision techniques. While these technologies have recently been extended from donors to acceptors, the extent to which kinetics will impact single-acceptor incorporation has yet to be assessed. We develop and apply an atomistic model for the single-acceptor incorporation rates of several recently demonstrated precursor molecules: diborane (B2H6), boron trichloride (BCl3), and aluminum trichloride in both monomer (AlCl3) and dimer forms (Al2Cl6), to identify the acceptor precursor and dosing conditions most likely to yield deterministic incorporation. While all three precursors can achieve single-acceptor incorporation, we predict that diborane is unlikely to achieve deterministic incorporation, boron trichloride can achieve deterministic incorporation with modest heating (50 °C), and aluminum trichloride can achieve deterministic incorporation at room temperature. We conclude that both boron and aluminum trichloride are promising precursors for atomic-precision single-acceptor applications, with the potential to enable the reliable production of large arrays of single-atom quantum devices.

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Quadrupolar interactions between acceptor pairs in p -doped semiconductors

Cited by 7 publications

References 54 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

Multihole models for deterministically placed acceptor arrays in silicon

Hole in one: Pathways to deterministic single-acceptor incorporation in Si(100)-2$\times$1

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