Analytic solutions for the valence subband mixing at the zone center of a GaAs/AlxGa1-xAs quantum well under uniaxial stress perpendicular to the growth direction

G. Rau, P. C. Klipstein, V. Nikos Nicopoulos, Neil F Johnson

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Using the envelope-function approach, we present a theoretical analysis of the effects of uniaxial stress applied along the [100] direction on the zone-center valence states of a type-I GaAs/GaxAl1-xAs [001] quantum well. The resulting strain reduces the symmetry and causes mixing between heavy and light holes which can be described approximately within the Γ8 subspace by a 4×4 Luttinger-Kohn Hamiltonian in conjunction with the correct 4×4 Bir-Pikus strain Hamiltonian. An approximate analytic solution is found by expanding the finite-stress solutions in terms of the zero-stress eigenstates. This representation allows a detailed analysis of the strain-induced coupling terms between heavy and light holes. By neglecting all small coupling terms it is possible to describe the hole mixing at any stress in terms of independent two-level systems. In this case the Hamiltonian becomes block diagonal and can easily be diagonalized analytically. Within the experimentally accessible pressure range of 10 kbar, these simple analytic solutions deviate from the large-scale numerical solutions by less than 1%. The coupling of the spin-orbit split-off states in the Γ7 subspace to the Γ8 subspace at finite and zero stress is then taken into account via second-order perturbation theory. Comparison of the theoretical results with experimental photoluminescence data shows good agreement and provides strong evidence for the stress-induced hole mixing.

Original languageEnglish (US)
Pages (from-to)5700-5711
Number of pages12
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume54
Issue number8
StatePublished - Aug 15 1996
Externally publishedYes

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Semiconductor quantum wells
quantum wells
valence
Hamiltonians
Direction compound
gallium arsenide
Photoluminescence
eigenvectors
Orbits
envelopes
perturbation theory
orbits
photoluminescence
causes
symmetry

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Analytic solutions for the valence subband mixing at the zone center of a GaAs/AlxGa1-xAs quantum well under uniaxial stress perpendicular to the growth direction. / Rau, G.; Klipstein, P. C.; Nikos Nicopoulos, V.; Johnson, Neil F.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 54, No. 8, 15.08.1996, p. 5700-5711.

Research output: Contribution to journalArticle

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abstract = "Using the envelope-function approach, we present a theoretical analysis of the effects of uniaxial stress applied along the [100] direction on the zone-center valence states of a type-I GaAs/GaxAl1-xAs [001] quantum well. The resulting strain reduces the symmetry and causes mixing between heavy and light holes which can be described approximately within the Γ8 subspace by a 4×4 Luttinger-Kohn Hamiltonian in conjunction with the correct 4×4 Bir-Pikus strain Hamiltonian. An approximate analytic solution is found by expanding the finite-stress solutions in terms of the zero-stress eigenstates. This representation allows a detailed analysis of the strain-induced coupling terms between heavy and light holes. By neglecting all small coupling terms it is possible to describe the hole mixing at any stress in terms of independent two-level systems. In this case the Hamiltonian becomes block diagonal and can easily be diagonalized analytically. Within the experimentally accessible pressure range of 10 kbar, these simple analytic solutions deviate from the large-scale numerical solutions by less than 1{\%}. The coupling of the spin-orbit split-off states in the Γ7 subspace to the Γ8 subspace at finite and zero stress is then taken into account via second-order perturbation theory. Comparison of the theoretical results with experimental photoluminescence data shows good agreement and provides strong evidence for the stress-induced hole mixing.",
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