Matrix elements in quantum{ region{} }¶
interband_matrix_elements{} (optional)¶
Provides the option to calculate interband matrix elements between wave functions of two different bands.
- output_matrix_elements (optional)
If
output_matrix_elements = yes
then matrix elements are saved in output file.
- type:
choice
- values:
yes
orno
- default:
yes
- output_transition_energies (optional)
If
output_transition_energies = yes
then transition energies are saved in output file.
- type:
choice
- values:
yes
orno
- default:
no
- KP6_Gamma{} (optional)
\(\sum_k \langle kp6_{k,i} | \Gamma_j \rangle\) , with k = 1 .. 6 indexing the component of the six-component \(\mathbf{k} \cdot \mathbf{p}\) wave function and \(i\), \(j\) indexing the wave function numbers.
kp_6band{}
andGamma{}
calculation must be present.- HH_Gamma{} (optional)
Matrix element of the transition between the heavy hole valence band and the gamma conduction band \(\langle HH_{i} | \Gamma_j \rangle\)
- LH_Gamma{} (optional)
Matrix element of the transition between the light hole valence band and the gamma conduction band \(\langle LH_{i} | \Gamma_j \rangle\)
- SO_Gamma{} (optional)
Matrix element of the transition between the split-off hole valence band and the gamma conduction band \(\langle SO_{i} | \Gamma_j \rangle\)
- HH_Delta{} (optional)
Matrix element of the transition between the heavy hole valence band and the Delta conduction band \(\langle LH_{i} | \Delta_j \rangle\)
- LH_Delta{} (optional)
Matrix element of the transition between the light hole valence band and the Delta conduction band \(\langle LH_{i} | \Delta_j \rangle\)
- SO_Delta{} (optional)
Matrix element of the transition between the split-off hole valence band and the Delta conduction band \(\langle SO_{i} | \Delta_j \rangle\)
- HH_X{} (optional)
Matrix element of the transition between the heavy hole valence band and the X conduction band \(\langle HH_{i} | X_j \rangle\)
- LH_X{} (optional)
Matrix element of the transition between the light hole valence band and the X conduction band \(\langle LH_{i} | X_j \rangle\)
- SO_X{} (optional)
Matrix element of the transition between the split-off valence band and the X conduction band \(\langle SO_{i} | X_j \rangle\)
- HH_L{} (optional)
Matrix element of the transition between the heavy hole valence band and the L conduction band \(\langle HH_{i} | L_j \rangle\)
- LH_L{} (optional)
Matrix element of the transition between the light hole valence band and the L conduction band \(\langle LH_{i} | L_j \rangle\)
- SO_L{} (optional)
Matrix element of the transition between the split-off valence band and the L conduction band \(\langle SO_{i} | L_j \rangle\)
intraband_matrix_elements{} (optional)¶
Calculate intraband matrix elements \(\langle i | \epsilon\cdot\hat{\mathbf{p}} | j \rangle\) for wave functions within one band. The light polarization direction \(\epsilon\) is automatically normalized in the program. \(\hat{\mathbf{p}} = i\hbar\nabla\) is the momentum vector.
For further reading: J. H. Davies, The Physics of Low-Dimensional Semiconductors. An Introduction, 2006, Chapters 10 and 8.
- name (optional)
defines suffix for related output files
- type:
string
- direction (optional)
It defines the polarization direction \(\epsilon\). From it a vector of unit length is calculated, which enters the calculation. In 1D simulation it can be omitted and [1,0,0] is then assumed.
- value:
3D real vector
- default:
[1 , 0 , 0]
- output_matrix_elements (optional)
If
output_matrix_elements = yes
then matrix elements are saved in output file.
- type:
choice
- values:
yes
orno
- default:
yes
- output_transition_energies (optional)
If
output_transition_energies = yes
then transition energies are saved in output file.
- type:
choice
- values:
yes
orno
- default:
no
- output_oscillator_strengths (optional)
If
output_oscillator_strengths = yes
then oscillator strengths are saved in output file.Currently, only a simple formula is used, i.e. the free electron mass is used and not the real effective mass one.
- type:
choice
- values:
yes
orno
- default:
no
- Gamma{} (optional)
Calculates the matrix element \(\langle \Gamma_i | \epsilon\cdot\hat{\mathbf{p}} | \Gamma_j \rangle\).
- X{} (optional)
Calculates the matrix element \(\langle X_i | \epsilon\cdot\hat{\mathbf{p}} | X_j \rangle\).
- Delta{} (optional)
Calculates the matrix element \(\langle \Delta_i | \epsilon\cdot\hat{\mathbf{p}} | \Delta_j \rangle\).
- L{} (optional)
Calculates the matrix element \(\langle L_i | \epsilon\cdot\hat{\mathbf{p}} | L_j \rangle\).
- HH{} (optional)
Calculates the matrix element \(\langle HH_i | \epsilon\cdot\hat{\mathbf{p}} | HH_j \rangle\).
- LH{} (optional)
Calculates the matrix element \(\langle LH_i | \epsilon\cdot\hat{\mathbf{p}} | LH_j \rangle\).
- SO{} (optional)
Calculates the matrix element \(\langle SO_i | \epsilon\cdot\hat{\mathbf{p}} | SO_j \rangle\).
- KP6{} (optional)
Calculates the matrix element \(\sum_k \langle kp6_{k,i} | \epsilon\cdot\hat{\mathbf{p}} | kp6_{k,j} \rangle\), \(k\) = 1,…,6.
- KP8{} (optional)
Calculates the matrix element \(\sum_k \langle kp8_{k,i} | \epsilon\cdot\hat{\mathbf{p}} | kp8_{k,j} \rangle\), \(k\) = 1,…,8.
dipole_moment_matrix_elements{} (optional)¶
Calculate dipole moment matrix elements \(\langle i | \epsilon\cdot\hat{\mathbf{d}} | j \rangle\) for wave functions within one band. The light polarization direction \(\epsilon\) is automatically normalized in the program. \(\hat{\mathbf{d}} = e\hat{\mathbf{r}}\) is the dipole moment vector.
For further reading: J. H. Davies, The Physics of Low-Dimensional Semiconductors. An Introduction, 2006, Chapters 10 and 8.
- name (optional)
defines suffix for related output files
- type:
string
- direction (optional)
It defines the polarization direction \(\epsilon\). From it a vector of unit length is calculated, which enters the calculation. In 1D simulation it can be omitted and [1,0,0] is then assumed.
- value:
3D real vector
- default:
[1 , 0 , 0]
- output_matrix_elements (optional)
If
output_matrix_elements = yes
then matrix elements are saved in output file.
- type:
choice
- values:
yes
orno
- default:
yes
- output_transition_energies (optional)
If
output_transition_energies = yes
then transition energies are saved in output file.
- type:
choice
- values:
yes
orno
- default:
no
- output_oscillator_strengths (optional)
If
output_oscillator_strengths = yes
then oscillator strengths are saved in output file.Currently, only a simple formula is used, i.e. the free electron mass is used and not the real effective mass one.
- type:
choice
- values:
yes
orno
- default:
no
- Gamma{} (optional)
Calculates the matrix element \(\langle \Gamma_i | \epsilon\cdot\hat{\mathbf{d}} | \Gamma_j \rangle\).
- X{} (optional)
Calculates the matrix element \(\langle X_i | \epsilon\cdot\hat{\mathbf{d}} | X_j \rangle\).
- Delta{} (optional)
Calculates the matrix element \(\langle \Delta_i | \epsilon\cdot\hat{\mathbf{d}} | \Delta_j \rangle\).
- L{} (optional)
Calculates the matrix element \(\langle L_i | \epsilon\cdot\hat{\mathbf{d}} | L_j \rangle\).
- HH{} (optional)
Calculates the matrix element \(\langle HH_i | \epsilon\cdot\hat{\mathbf{d}} | HH_j \rangle\).
- LH{} (optional)
Calculates the matrix element \(\langle LH_i | \epsilon\cdot\hat{\mathbf{d}} | LH_j \rangle\).
- SO{} (optional)
Calculates the matrix element \(\langle SO_i | \epsilon\cdot\hat{\mathbf{d}} | SO_j \rangle\).
- KP6{} (optional)
Calculates the matrix element \(\sum_k \langle kp6_{k,i} | \epsilon\cdot\hat{\mathbf{d}} | kp6_{k,j} \rangle\), \(k\) = 1,…,6.
- KP8{} (optional)
Calculates the matrix element \(\sum_k \langle kp8_{k,i} | \epsilon\cdot\hat{\mathbf{d}} | kp8_{k,j} \rangle\), \(k\) = 1,…,8.