Diagonal parameter shifts due to nearest-neighbor displacements in empirical tight-binding theory

Boykin, Timothy B.; Klimeck, Gerhard; Bowen, R. Chris; Oyafuso, Fabiano

doi:10.1103/physrevb.66.125207

Cited by 236 publications

(214 citation statements)

References 15 publications

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“…The present tight-binding model includes sp 3 d 5 s * basis orbitals. 51 Therefore, the total electron density at nuclear site R j is given by s-symmetry orbital densities:…”

Section: ͑2͒mentioning

confidence: 99%

“…55 Following the strain calculation, the electron wave function in the strained nanostructure is obtained with the empirical sp 3 d 5 s * tight-binding model including the spinorbit coupling. 51 The strain effect on the electronic structure is captured by adjusting the atomic energies of the tightbinding model with a linear correction that is obtained within the Löwdin orthogonalization procedure. 51,56 We also modify the nearest-neighbor coupling parameters for the strained structures according to the generalized version of Harrison's d 2 scaling law and the Slater-Koster direction-cosine rule.…”

Section: ͑2͒mentioning

confidence: 99%

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Effect of electron-nuclear spin interactions for electron-spin qubits localized in InGaAs self-assembled quantum dots

Lee

Allmen

Oyafuso

et al. 2005

Journal of Applied Physics

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Lee, Seungwon; von Allmen, Paul; Oyafuso, Fabiano; and Klimeck, Gerhard, "Effect of electron-nuclear spin interactions for electronspin qubits localized in InGaAs self-assembled quantum dots" (2005 The effect of electron-nuclear spin interactions on qubit operations is investigated for a qubit represented by the spin of an electron localized in an InGaAs self-assembled quantum dot. The localized electron wave function is evaluated within the atomistic tight-binding model. The electron Zeeman splitting induced by the electron-nuclear spin interaction is estimated in the presence of an inhomogeneous environment characterized by a random nuclear spin configuration, by the dot-size distribution, alloy disorder, and interface disorder. Due to these inhomogeneities, the electron Zeeman splitting varies from one qubit to another by the order of 10 −6 , 10 −6 , 10 −7 , and 10 −9 eV, respectively. Such fluctuations cause errors in exchange operations due to the inequality of the Zeeman splitting between two qubits. However, the error can be made lower than the quantum error threshold if an exchange energy larger than 10 −4 eV is used for the operation. This result shows that the electron-nuclear spin interaction does not hinder quantum-dot based quantum computer architectures from being scalable even in the presence of inhomogeneous environments.

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“…The present tight-binding model includes sp 3 d 5 s * basis orbitals. 51 Therefore, the total electron density at nuclear site R j is given by s-symmetry orbital densities:…”

Section: ͑2͒mentioning

confidence: 99%

Section: ͑2͒mentioning

confidence: 99%

Effect of electron-nuclear spin interactions for electron-spin qubits localized in InGaAs self-assembled quantum dots

Lee

Allmen

Oyafuso

et al. 2005

Journal of Applied Physics

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“…The Hamiltonian matrix elements are obtained by fitting to experimental bulk band structure parameters with a genetic optimization algorithm. [3,14] To take into account the effect of the displacements of atoms from the unstrained crystal positions, the atomic energies (the diagonal elements of the Hamiltonian) are adjusted by a linear correction within the Löwdin orthogonalization procedure. [14,15] The coupling parameters between nearest-neighbor orbitals (the off-diagonal elements of the Hamiltonian) are also modified according to the generalized Harrison d −2 scaling law and Slater-Koster direction-cosine rules.…”

Section: Nanostructure Modelingmentioning

confidence: 99%

“…[3,14] To take into account the effect of the displacements of atoms from the unstrained crystal positions, the atomic energies (the diagonal elements of the Hamiltonian) are adjusted by a linear correction within the Löwdin orthogonalization procedure. [14,15] The coupling parameters between nearest-neighbor orbitals (the off-diagonal elements of the Hamiltonian) are also modified according to the generalized Harrison d −2 scaling law and Slater-Koster direction-cosine rules. [16,17] The eigenvalues of the tight-binding Hamiltonian is obtained with the Lanczos algorithm, [18] which is a commonly used iterative eigenvalue solver for large-dimensional, sparse, Hermitian matrices, as is the case for our tight-binding Hamiltonian.…”

Section: Nanostructure Modelingmentioning

confidence: 99%

Boundary conditions for the electronic structure of finite-extent embedded semiconductor nanostructures

et al. 2004

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The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires a proper boundary treatment for a finite simulation domain. For the study of a selfassembled InAs dot embedded in GaAs, three kinds of boundary conditions are examined within the empirical tight-binding model: (i) the periodic boundary condition, (ii) raising the orbital energies of surface atoms, and (iii) raising the energies of dangling bonds at the surface. The periodic boundary condition requires a smooth boundary and consequently a larger GaAs buffer than the two non-periodic boundary conditions. Between the non-periodic conditions, the dangling-bond energy shift is more numerically efficient than the orbital-energy shift, in terms of the elimination of non-physical surface states in the energy region of interest for interior states. A dangling-bond energy shift larger than 5 eV efficiently eliminates all of the surface states and leads to interior states that are highly insensitive to the choice of the energy shift.

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“…The primary advantage of the nearestneighbor sp 3 d 5 s * model is its straightforward incorporation of strain distortions. 11 In the donor description below, no strain distortions are considered, and the second-neighbor model P085 provides an unprecedented representation of the Si CB.…”

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Conduction-band tight-binding description for Si applied to P donors

et al. 2005

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Diagonal parameter shifts due to nearest-neighbor displacements in empirical tight-binding theory

Cited by 236 publications

References 15 publications

Effect of electron-nuclear spin interactions for electron-spin qubits localized in InGaAs self-assembled quantum dots

Effect of electron-nuclear spin interactions for electron-spin qubits localized in InGaAs self-assembled quantum dots

Boundary conditions for the electronic structure of finite-extent embedded semiconductor nanostructures

Conduction-band tight-binding description for Si applied to P donors

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