The Four-Band Spin-Less Kane Model in Curvilinear Coordinates

Jens Gravesen, Morten Willatzen*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The possibility to fabricate complicated nanostructure geometries with novel topological effects so as to tailor physical properties makes it adamant to develop advanced analytical and numerical methods. The first multiband k · p model in general curvilinear coordinates based on Kane's four‐band spin‐less model for the upper conduction and valence band states is developed. The model captures the combined effects of electron and light‐hole bandstructure coupling and curvature effects. The formulation in curvilinear coordinates allows to obtain a simple set of equations, displaying directly the influence of the local curvature, and the explicit equation sets in the cases of a torus and a helix‐shaped nanowire structure with a square cross section are given. The presented derivation can be generalized to other types of k · p multiband models.
Original languageEnglish
Article number1800305
JournalPhysica Status Solidi. Rapid Research Letters
Volume13
Issue number1
Number of pages5
ISSN1862-6254
DOIs
Publication statusPublished - 2019

Keywords

  • Four‐band spin‐less Kane model
  • General coordinates
  • k ·  p model

Cite this

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title = "The Four-Band Spin-Less Kane Model in Curvilinear Coordinates",
abstract = "The possibility to fabricate complicated nanostructure geometries with novel topological effects so as to tailor physical properties makes it adamant to develop advanced analytical and numerical methods. The first multiband k · p model in general curvilinear coordinates based on Kane's four‐band spin‐less model for the upper conduction and valence band states is developed. The model captures the combined effects of electron and light‐hole bandstructure coupling and curvature effects. The formulation in curvilinear coordinates allows to obtain a simple set of equations, displaying directly the influence of the local curvature, and the explicit equation sets in the cases of a torus and a helix‐shaped nanowire structure with a square cross section are given. The presented derivation can be generalized to other types of k · p multiband models.",
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The Four-Band Spin-Less Kane Model in Curvilinear Coordinates. / Gravesen, Jens; Willatzen, Morten.

In: Physica Status Solidi. Rapid Research Letters, Vol. 13, No. 1, 1800305, 2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - The Four-Band Spin-Less Kane Model in Curvilinear Coordinates

AU - Gravesen, Jens

AU - Willatzen, Morten

PY - 2019

Y1 - 2019

N2 - The possibility to fabricate complicated nanostructure geometries with novel topological effects so as to tailor physical properties makes it adamant to develop advanced analytical and numerical methods. The first multiband k · p model in general curvilinear coordinates based on Kane's four‐band spin‐less model for the upper conduction and valence band states is developed. The model captures the combined effects of electron and light‐hole bandstructure coupling and curvature effects. The formulation in curvilinear coordinates allows to obtain a simple set of equations, displaying directly the influence of the local curvature, and the explicit equation sets in the cases of a torus and a helix‐shaped nanowire structure with a square cross section are given. The presented derivation can be generalized to other types of k · p multiband models.

AB - The possibility to fabricate complicated nanostructure geometries with novel topological effects so as to tailor physical properties makes it adamant to develop advanced analytical and numerical methods. The first multiband k · p model in general curvilinear coordinates based on Kane's four‐band spin‐less model for the upper conduction and valence band states is developed. The model captures the combined effects of electron and light‐hole bandstructure coupling and curvature effects. The formulation in curvilinear coordinates allows to obtain a simple set of equations, displaying directly the influence of the local curvature, and the explicit equation sets in the cases of a torus and a helix‐shaped nanowire structure with a square cross section are given. The presented derivation can be generalized to other types of k · p multiband models.

KW - Four‐band spin‐less Kane model

KW - General coordinates

KW - k ·  p model

U2 - 10.1002/pssr.201800305

DO - 10.1002/pssr.201800305

M3 - Journal article

VL - 13

JO - Physica Status Solidi. Rapid Research Letters

JF - Physica Status Solidi. Rapid Research Letters

SN - 1862-6254

IS - 1

M1 - 1800305

ER -