TransmissionEigenvalues

	TransmissionEigenvalues
TransmissionPathways	TransmissionEigenstate

Name

TransmissionEigenvalues — Class for representing the transmission eigenvalues for a given configuration and calculator.

Synopsis

Namespace: NanoLanguage

TransmissionEigenvalues(
configuration,
energy,
k_point,
energy_zero_parameter
)

Description

Constructor for the TransmissionEigenvalues object.

TransmissionEigenvalues Arguments

configuration

The two-probe configuration with attached calculator for which the transmission eigenvalues should be calculated.

Type: A DeviceConfiguration.

Default:


          None

energy

The energy for which the transmission eigenvalues should be calculated.

Type: A value of the type PhysicalQuantity of with energy unit.

Default:


          0.0*eV

k_point

The 2-dimensional k-point for which the transmission eigenvalues should be calculated (x,y).

Type: A single list of floats with shape (1,2), i.e. [0.8, 0.2], in fractional coordinates.

Default:


          [0.0, 0.0]

energy_zero_parameter

Specifies the choice for the energy zero.

Type: AverageFermiLevel | AbsoluteEnergy | FermiLevel

Default:


          AverageFermiLevel

TransmissionEigenvalues Methods

A TransmissionEigenvalues object provides the following methods:

electrodeFermiLevels(): Return the electrodes Fermi levels in absolute energies.
energy(): Return the energy used in this transmission eigenvalue calculation.
energyZero(): Return the energy zero used for the energy scale in this transmission eigenvalue calculation.
energyZeroParameter(): Return the energy zero parameter used for setting the energy scale in this transmission eigenvalue calculation.
evaluate(spin): Obtain the calculated transmission eigenvalues.

spin

The spin component to evaluate.
Type: Spin.Up | Spin.Down
Default: Spin.Up
kPoint(): Return the k-point used in this transmission eigenvalue calculation.
nlprint(stream): Print a string containing an ASCII table of transmission eigenvalues.

stream

The stream the transmission eigenvalues should be written to.
Type: A stream that supports strings being written to using 'write'.
Default: sys.stdout

Usage Examples

Calculate the transmission eigenvalues for a device configuration and print out the result

eigenvalues = TransmissionEigenvalues(device_configuration,0.0*eV )
nlprint(eigenvalues)

Notes

The TransmissionEigenvalues is an analysis option which finds the eigenvalues of the transmission matrix. The transmission matrix, for a given energy $E$ and k-point $\mathbf{k}$ , is given by

$\displaystyle T_{nm}(E,\mathbf{k}) = \sum_\ell t_{n\ell}(E,\mathbf{k}) t^\dagger_{\ell m}(E,\mathbf{k}),$

where $t_{n\ell}(\mathbf{k})$ is the transmission amplitude from Bloch state $\psi_n(\mathbf{k})$ in the left electrode to Bloch state $\psi_\ell(\mathbf{k})$ in the right electrode.

The transmission coefficient is given by the trace of the transmission matrix

$\displaystyle T(E,\mathbf{k}) = \sum_n T_{nn}(E,\mathbf{k}).$

Below we will suppress the indices $E$ and $\mathbf{k}$ in most cases, but keep in mind that all quantities depend on these quantum numbers parametrically.

The transmission eigenvalues $\lambda_\alpha$ are the eigenvalues of the transmission matrix $T_{nm}$ .

It follows from the invariance of the trace of a matrix that the transmission eigenvalues sum up to the transmission coefficient,

$\displaystyle T = \sum_\alpha \lambda_\alpha .$

The transmission eigenvalues are in ATK in the range [0,1] for each spin channel.