Invariant expansion of the 30-band 
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 model and its parameters for III-V compounds

Gawarecki, Krzysztof; Scharoch, P.; Wiśniewski, Michał; Ziembicki, Jakub; Mączko, Herbert S.; Gładysiewicz, M.; Kudrawiec, R.

doi:10.1103/physrevb.105.045202

Cited by 6 publications

(5 citation statements)

References 90 publications

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“…For GaAs, Gawarecki and collaborators [130] show an excellent full zone agreement between model and DFT bands considering 30 bands. In contrast, our results presented in Fig.…”

Section: Full Zone Kpmentioning

confidence: 85%

“…The resulting effective models yield band structures that match well the DFT data in the low energy sector near the k point used for the wavefunction expansion. Therefore, our code provides an ab initio approach for the k • p numerical parameters, which can be contrasted with fitting methods [60,[76][77][78]130], in which the numerical coefficients are obtained by numerically minimizing the residue difference between the DFT and model band structures over a selected range of the Brillouin zone. These fitting procedures work well in general but require careful verification if the fitted parameters are reasonable.…”

Section: Discussionmentioning

confidence: 99%

“…Usually, one expects the resulting effective model to be valid only near k 0 and only for a small energy range that encloses the bands of interest. In contrast, within the full zone k • p approach [66,[126][127][128][129][130] one considers a large set of bands, such that the resulting low energy model agrees well with DFT or experimental bands over the full Brillouin zone, instead of only the vicinity of k 0 . However, to achieve this precision, one needs to apply fitting procedures to ensure that the bands match selected energy levels at various k points over the Brillouin zone.…”

Section: Full Zone Kpmentioning

confidence: 99%

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DFT2kp: Effective kp models from ab-initio data

V. Cassiano,

de Lelis Araújo,

Faria Junior

et al. 2024

SciPost Phys. Codebases

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The k\cdot pk⋅p method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator \pi= p+ p_{SOC}π=p+pSOC (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of k\cdot pk⋅p effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation UU that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a “hands-on” example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

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“…For GaAs, Gawarecki and collaborators [130] show an excellent full zone agreement between model and DFT bands considering 30 bands. In contrast, our results presented in Fig.…”

Section: Full Zone Kpmentioning

confidence: 85%

Section: Discussionmentioning

confidence: 99%

Section: Full Zone Kpmentioning

confidence: 99%

See 1 more Smart Citation

DFT2kp: Effective kp models from ab-initio data

V. Cassiano,

de Lelis Araújo,

Faria Junior

et al. 2024

SciPost Phys. Codebases

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show abstract

“…For example, a precise description of valence bands and the two lowest conduction bands of direct and indirect gap bulk semiconductors can be obtained with 24 × 24 basis [19]. Nonetheless, a 40 × 40 band k•p is enough to accurately reproduce the overall band structure of strained and unstrained semiconductor alloys [20,21]. Even a big 40 × 40 k•p Hamiltonian, from the quantum computer perspective, requires solely 6 qubits.…”

Section: Discussionmentioning

confidence: 99%

“…Since its development, the k • p method has been widely used to analyze the electronic structure of semiconductors in the vicinity of high-symmetry points of the Brillouin zone [19][20][21]. The method is grounded on the influence of the crystalline periodic potential profile over the electron in the structure, taking into account the effective mass approximation [22,23].…”

Section: The K • P Methodsmentioning

confidence: 99%

Revisiting semiconductor bulk hamiltonians using quantum computers

Pimenta

Bezerra

2023

Phys. Scr.

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With the advent of near-term quantum computers, it is now possible to simulate solid-state properties using quantum algorithms. By an adequate description of the system’s Hamiltonian, variational methods enable to fetch of the band structure and other fundamental properties as transition probabilities. Here, we describe semiconductor structures of the III-V family using k$\cdot$p Hamiltonians and obtain their band structures using a state vector solver, a probabilistic simulator, and a real noisy-device simulator. The resulting band structures are in good agreement with those obtained by direct diagonalization of the Hamiltonian. The simulation times depend on the optimizer, circuit depth, and simulator used. Finally, with the optimized eigenstates, we convey the inter-band absorption probability, demonstrating the possibility of analyzing the fundamental properties of crystalline systems using quantum computers.

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Analyzing k · p modeling in highly mismatched alloys and other III–V semiconductors

Gladysiewicz,

Wartak

2023

Journal of Applied Physics

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This Tutorial provides a comprehensive overview of various k⋅p models used to describe the electronic band structures of semiconductors with cubic diamond and zinc blende symmetries. Our primary focus is on III–V semiconductors, with a particular emphasis on highly mismatched alloys. We begin our exploration with the six-band k⋅p model, which effectively captures interactions within the highest valence bands. Following that, we delve into the intricacies of the eight-band k⋅p model, which takes into account strain effects and modifications to energy dispersion. The Tutorial also introduces the band anticrossing model and its corresponding ten-band k⋅p models, specifically tailored for dilute nitride semiconductors. Furthermore, we extend our discussion to the valence band anticrossing model and its application to the 14-band k⋅p model in the context of dilute bismide materials. Additionally, we emphasize the significance of more comprehensive models, exemplified by the 30-band k⋅p model, for faithfully representing the entire Brillouin zone.

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Invariant expansion of the 30-band k·p model and its parameters for III-V compounds

Cited by 6 publications

References 90 publications

DFT2kp: Effective kp models from ab-initio data

DFT2kp: Effective kp models from ab-initio data

Revisiting semiconductor bulk hamiltonians using quantum computers

Analyzing k · p modeling in highly mismatched alloys and other III–V semiconductors

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