### 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/Ga_{x}Al_{1-x}As [001] quantum well. The resulting strain reduces the symmetry and causes mixing between heavy and light holes which can be described approximately within the Γ_{8} 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 Γ_{7} subspace to the Γ_{8} 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 language | English (US) |
---|---|

Pages (from-to) | 5700-5711 |

Number of pages | 12 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 54 |

Issue number | 8 |

State | Published - Aug 15 1996 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

_{x}Ga

_{1-x}As quantum well under uniaxial stress perpendicular to the growth direction.

*Physical Review B - Condensed Matter and Materials Physics*,

*54*(8), 5700-5711.

**Analytic solutions for the valence subband mixing at the zone center of a GaAs/Al _{x}Ga_{1-x}As quantum well under uniaxial stress perpendicular to the growth direction.** / Rau, G.; Klipstein, P. C.; Nikos Nicopoulos, V.; Johnson, Neil F.

Research output: Contribution to journal › Article

_{x}Ga

_{1-x}As quantum well under uniaxial stress perpendicular to the growth direction',

*Physical Review B - Condensed Matter and Materials Physics*, vol. 54, no. 8, pp. 5700-5711.

_{x}Ga

_{1-x}As quantum well under uniaxial stress perpendicular to the growth direction. Physical Review B - Condensed Matter and Materials Physics. 1996 Aug 15;54(8):5700-5711.

}

TY - JOUR

T1 - 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

AU - Rau, G.

AU - Klipstein, P. C.

AU - Nikos Nicopoulos, V.

AU - Johnson, Neil F

PY - 1996/8/15

Y1 - 1996/8/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001566256&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001566256&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001566256

VL - 54

SP - 5700

EP - 5711

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 8

ER -