intraband_matrix_elements{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculate intraband matrix elements $⟨i|ϵ\cdot \hat{\mathbf{p}}|j⟩$ for wave functions within one band. The light polarization direction $ϵ$ is automatically normalized in the program. $\hat{\mathbf{p}}=i\hslash \mathrm{\nabla }$ is the momentum vector.

For further reading: J. H. Davies, The Physics of Low-Dimensional Semiconductors. An Introduction, 2006, Chapters 10 and 8.

Nested keywords

name direction Gamma{ } X{ } Delta{ }

L{ } HH{ } LH{ } SO{ } KP6{ }

KP8{ } output_matrix_elements output_transition_energies output_oscillator_strengths

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name

Calling sequence

quantum{ region{ intraband_matrix_elements{ name = ... } } }

Properties

• usage: $\mathrm{optional}$

• type: character string

Functionality

defines suffix for related output files

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direction

Calling sequence

quantum{ region{ intraband_matrix_elements{ direction = [ ..., ..., ... ] } } }

Properties

• usage: $\mathrm{optional}$

• 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: $-$

Functionality

It defines the polarization direction $ϵ$. 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.

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output_matrix_elements

Calling sequence

quantum{ region{ intraband_matrix_elements{ output_matrix_elements = ... } } }

Properties

• usage: $\mathrm{optional}$

• type: choice

• values: yes or no

• default: yes

Functionality

If output_matrix_elements = yes then matrix elements are saved in output file.

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output_transition_energies

Calling sequence

quantum{ region{ intraband_matrix_elements{ output_transition_energies = ... } } }

Properties

• usage: $\mathrm{optional}$

• type: choice

• values: yes or no

• default: no

Functionality

If output_transition_energies = yes then transition energies are saved in output file.

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output_oscillator_strengths

Calling sequence

quantum{ region{ intraband_matrix_elements{ output_oscillator_strengths = ... } } }

Properties

• usage: $\mathrm{optional}$

• type: choice

• values: yes or no

• default: 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.

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Gamma{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ Gamma{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $⟨{\mathrm{\Gamma }}_i|ϵ\cdot \hat{\mathbf{p}}|{\mathrm{\Gamma }}_j⟩$.

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X{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ X{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $⟨X_i|ϵ\cdot \hat{\mathbf{p}}|X_j⟩$.

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Delta{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ Delta{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $⟨{\mathrm{\Delta }}_i|ϵ\cdot \hat{\mathbf{p}}|{\mathrm{\Delta }}_j⟩$.

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L{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ L{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $⟨L_i|ϵ\cdot \hat{\mathbf{p}}|L_j⟩$.

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HH{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ HH{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $⟨H{H}_i|ϵ\cdot \hat{\mathbf{p}}|H{H}_j⟩$.

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LH{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ LH{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $⟨L{H}_i|ϵ\cdot \hat{\mathbf{p}}|L{H}_j⟩$.

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SO{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ SO{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $⟨S{O}_i|ϵ\cdot \hat{\mathbf{p}}|S{O}_j⟩$.

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KP6{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ KP6{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $\sum _k⟨kp{6}_{k,i}|ϵ\cdot \hat{\mathbf{p}}|kp{6}_{k,j}⟩$, $k$ = 1,…,6.

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KP8{ }

Calling sequence

quantum{ region{ intraband_matrix_elements{ KP8{ } } } }

Properties

• usage: $\mathrm{optional}$

• items: maximum 1

Functionality

Calculates the matrix element $\sum _k⟨kp{8}_{k,i}|ϵ\cdot \hat{\mathbf{p}}|kp{8}_{k,j}⟩$, $k$ = 1,…,8.

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Last update: 17/04/2025