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Position operators and interband matrix elements of scalar and vector potentials in the 8-band Kane model
by I. A. Ado, M. Titov, Rembert A. Duine, Arne Brataas
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Submission summary
| Authors (as registered SciPost users): | Ivan Ado |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2312.09349v3 (pdf) |
| Date accepted: | 2024-05-28 |
| Date submitted: | 2024-05-24 19:21 |
| Submitted by: | Ado, Ivan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We diagonalize the 8-band Kane Hamiltonian with a proper inclusion of the interband matrix elements of the scalar and vector potentials. This leads, among other results, to a modification of the conventional expression for the spin-orbit coupling (SOC) strength in narrow-gap semiconductors with the zinc blende symmetry. We find that in GaAs, at low temperatures, the correct expression for the SOC strength is actually twice as large as usually considered. In InSb it is $1.76$ times larger. We also provide a proper treatment of the interband matrix elements of the position operator. We show that the velocity operator in a crystal should be defined as a time-derivative of a fictitious position operator rather than the physical one. We compute the expressions for both these position operators projected to the conduction band of the 8-band Kane model. We also derive an expression for the velocity operator and demonstrate that the SOC strength in it differs from the SOC strength in the Hamiltonian. The ratio between them is not equal to $1$, as it is often assumed for the Rashba model. It does not equal $2$ either. The correct result for this ratio is given by a rational function of the parameters of the model. This function takes values between $4(23+3\sqrt{2})/73\approx 1.49$ and $2$. Our findings modify a vast number of research results obtained using the Rashba model and provide a path for a consistent treatment of the latter in future applications.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
We added Sections 3.4 and 4.6. We significantly revised Section 4.5 and the second part of Section 2.1. We added a Table at the end of Section 3.3. We gave a proper credit to Phys. Rev. B 102, 075310 (2020).
Published as SciPost Phys. 17, 009 (2024)