momentum_matrix_elements{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculate polarization dependent momentum matrix elements \(\epsilon\cdot\langle \psi_i | \hat{\mathbf{p}} | \psi_j \rangle\) for wave functions within one band. The light polarization direction \(\epsilon\) is automatically normalized in the program.
For further reading: J. H. Davies, The Physics of Low-Dimensional Semiconductors. An Introduction, 2006, Chapters 10 and 8.
Nested keywords
polarization{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ polarization{ } } } }
Properties
usage: \(\mathrm{\textcolor{WildStrawberry}{required}}\)
items: no constraints
Functionality
Defines complex polarization vector of the incident light for the model, here based on the Fermi’s golden rule.
polarization{ name }
Calling sequence
quantum{ region{ momentum_matrix_elements{ polarization{ name = "..." } } } }
Properties
usage: \(\mathrm{\textcolor{WildStrawberry}{required}}\)
type: character string
Functionality
Defines suffix for all spectra output files related to the polarization defined in this group.
polarization{ re }
Calling sequence
quantum{ region{ momentum_matrix_elements{ polarization{ re = [ ..., ..., ... ] } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: vector of 3 real numbers: \((r_1, r_2, r_3)\)
values: no constraints
default: \(r_1=1.0\), \(r_2=0.0\), \(r_3=0.0\)
unit: \(\mathrm{-}\)
Functionality
Defines real part of the polarization versor \(\epsilon\). Normalized vector of unit length is calculated based on both real and imaginary parts, which enters the calculation.
polarization{ re }
Calling sequence
quantum{ region{ momentum_matrix_elements{ polarization{ im = [ ..., ..., ... ] } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: vector of 3 real numbers: \((r_1, r_2, r_3)\)
values: no constraints
default: \(r_1=0.0\), \(r_2=0.0\), \(r_3=0.0\)
unit: \(\mathrm{-}\)
Functionality
Defines imaginary part of the polarization versor \(\epsilon\). Normalized vector of unit length is calculated based on both real and imaginary parts, which enters the calculation.
all_k_points
Calling sequence
quantum{ region{ momentum_matrix_elements{ all_k_points = ... } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: choice
values:
yesornodefault:
yes
Functionality
If all_k_points = yes then matrix elements are outputted for all simulation k-points used in integration of densities of states.
Gamma{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ Gamma{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\langle \Gamma_i | \epsilon\cdot\hat{\mathbf{p}} | \Gamma_j \rangle\).
X{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ X{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\langle X_i | \epsilon\cdot\hat{\mathbf{p}} | X_j \rangle\).
Delta{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ Delta{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\langle \Delta_i | \epsilon\cdot\hat{\mathbf{p}} | \Delta_j \rangle\).
L{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ L{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\langle L_i | \epsilon\cdot\hat{\mathbf{p}} | L_j \rangle\).
HH{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ HH{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\langle HH_i | \epsilon\cdot\hat{\mathbf{p}} | HH_j \rangle\).
LH{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ LH{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\langle LH_i | \epsilon\cdot\hat{\mathbf{p}} | LH_j \rangle\).
SO{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ SO{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\langle SO_i | \epsilon\cdot\hat{\mathbf{p}} | SO_j \rangle\).
KP6{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ KP6{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\sum_k \langle kp6_{k,i} | \epsilon\cdot\hat{\mathbf{p}} | kp6_{k,j} \rangle\), \(k\) = 1,…,6.
KP8{ }
Calling sequence
quantum{ region{ momentum_matrix_elements{ KP8{ } } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1
Functionality
Calculates the matrix element \(\sum_k \langle kp8_{k,i} | \epsilon\cdot\hat{\mathbf{p}} | kp8_{k,j} \rangle\), \(k\) = 1,…,8.
output_matrix_elements
Calling sequence
quantum{ region{ momentum_matrix_elements{ output_matrix_elements = ... } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: choice
values:
yesornodefault:
yes
Functionality
If output_matrix_elements = yes then matrix elements are saved in output file.
output_oscillator_strengths
Calling sequence
quantum{ region{ momentum_matrix_elements{ output_oscillator_strengths = ... } } }
Properties
usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: choice
values:
yesornodefault:
no
Functionality
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.
Last update: 2025/07/15