Energy contour parameters

The parameters here are for setting up the contour integration over energy for calculating the density matrix from the Green’s functions.

calculation.complexEcontour.type

keyword: calculation.complexEcontour.type

possible values: ‘smallSemiCircle’, ‘middleSemiCircle’, ‘largeSemiCircle’, ‘doubleSemiCircle’

default value: ‘smallSemiCircle’

description: Type of energy contour to be used in the integration of the equilibrium part of lesser Green’s function. See user manual for more information about the choice of complex contour.

an example:

calculation.complexEcontour.type = 'smallSemiCircle'
'largeSemiCircle', 'doubleSemiCircle'

calculation.complexEcontour.numberOfPoints

keyword: calculation.complexEcontour.numberOfPoints

possible values: an integer

default value: 20, 40, or 60, depending on the value of the parameter calculation.control.precision.

description: Number of energy points used on the complex energy contour for integrating the equilibrium part of the lesser Green’s function. (Note: if the system temperature is not zero, numberOfPoints is the number of energy points on the circle part of the contour.)

an example:

calculation.complexEcontour.numberOfPoints = 40

calculation.complexEcontour.lowestEnergyPoint

keyword: calculation.complexEcontour.lowestEnergyPoint

possible values: a double number with proper energy unit such as ‘eV’, ‘Ryd’, ‘Ryd.’, ‘Rydberg’, ‘au’, ‘a.u.’, ‘atomic unit’, ‘Hartree’, where ‘au’ ‘a.u.’, and ‘atomic unit’ are for Hartree, ‘Ryd’, ‘Ryd.’ for Rydberg.

default value: determined by nanodcal

description: The lowest energy point on the complex energy contour. Note that if the number part of the input is missing, it will be considered as 1; if the unit part is missing, it will be considered as using the unit defined by calculation.control.energyUnit.

an example:

calculation.complexEcontour.lowestEnergyPoint = 40

calculation.complexEcontour.Delta

keyword: calculation.complexEcontour.Delta

possible values: an integer

default value: 10

description: Used only in the finite temperature case. The number of poles of the Fermi function which are enclosed in the complex energy contour.

an example:

calculation.complexEcontour.Delta = 10

calculation.complexEcontour.gamma

keyword: calculation.complexEcontour.gamma

possible values: an integer

default value: 20

description: Used only in the finite temperature case. The length (in unit kT) of the straight portion of the complex energy contour that is below the Fermi energy.

an example:

calculation.complexEcontour.gamma = 20

calculation.complexEcontour.numberOfPoints2

keyword: calculation.complexEcontour.numberOfPoints2

possible values: an integer

default value: 4, 8, or 16, depending on the value of the parameter calculation.control.precision.

description: Used only in cases of finite temperature. The number of energy points on the straight part of the complex energy contour for integrating the equilibrium part of lesser Green’s function.

an example:

calculation.complexEcontour.numberOfPoints2 = 6

calculation.realEcontour.numberOfPoints

keyword: calculation.realEcontour.numberOfPoints

possible values: an integer

default value: determined using the value of realEcontour.interval

description: Number of energy points on the real energy axis for integrating the non-equilibrium part of lesser Green’s function.

an example:

calculation.realEcontour.numberOfPoints = 40

calculation.realEcontour.interval

keyword: calculation.realEcontour.interval

possible values: a double number with proper energy unit such as ‘eV’, ‘Ryd’, ‘Ryd.’, ‘Rydberg’, ‘au’, ‘a.u.’, ‘atomic unit’, ‘Hartree’, where ‘au’ ‘a.u.’, and ‘atomic unit’ are for Hartree, ‘Ryd’, ‘Ryd.’ for Rydberg.

default value: 2e-3, 5e-4, or 1e-4 Hartree, depending on the value of the parameter calculation.control.precision.

description: Energy interval used to determine the number of energy points for integrating the non-equilibrium part of lesser Green’s function on the real energy axis. This input is not used when realEcontour.numberOfPoints is given. Note that if the number part of the input is missing, it will be considered as 1; if the unit part is missing, it will be considered as using the unit defined by calculation.control.energyUnit.

an example:

calculation.realEcontour.interval = 5e-4 Hartree

calculation.transmission.isAveraged

keyword: calculation.transmission.isAveraged

possible values: 0, 1, 2

default value: 1

description: If 0, the calculated transmission coefficient is expressed as a function of both energy and transverse k-vector (i.e. gives transmission hot spot). If 1, in addition, a k-space average is performed on the transmission coefficient, and the averaged coefficient is a function of energy only. If 2, only the averaged transmission coefficient are kept, just for saving disk space.

an example:

calculation.transmission.isAveraged = 2

calculation.transmission.eigenChannelNumber

keyword: calculation.transmission.eigenChannelNumber

possible values: 0 or a positive integer

default value: 0

description: When it is a positive number, the transmission coefficient will be projected into the contributions of eigen-channels, and this positive integer should be an estimated upper-bound of the number of eigen-channels. resolved in k-space, instead of integrated over the Brillouin zone.

an example:

calculation.transmission.isProjected = true

calculation.transmission.kSpacePoints

keyword: calculation.transmission.kSpacePoints

possible values: 3\(\times\)n double array

default value: defined in the k-point file if the file is given by the parameter transmission.kPointFile, or produced by the parameters transmission.kSpaceGridNumber and transmission.kSpaceGridShift

description: the fractional coordinates of n transverse wave vectors at which the transmission will be calculated.

an example:

calculation.transmission.kSpacePoints = [0 0 0]

calculation.transmission.kPointWeights

keyword: calculation.transmission.kPointWeights

possible values: 1\(\times\)n double array

default value: defined in the k-point file if the corresponding parameter transmission.kSpacePoints is using the k-values in the same file. Otherwise, equally weighted.

description: the weights of the k-space points in the k-space integration.

an example:

calculation.transmission.kPointWeights = [1/2 1/3 1/6]

calculation.transmission.etaSigma

keyword: calculation.transmission.etaSigma

possible values: a small double number

default value: 1e-6 Hartree

description: the small eta used in the calculation of self-energy when the GreenFunction method is chosen.

an example:

calculation.transmission.etaSigma = 1e-4

calculation.transmission.etaGF

keyword: calculation.transmission.etaGF

possible values: a small double number

default value: 0

description: the small eta used in the calculation of Greens function when the GreenFunction method is chosen.

an example:

calculation.transmission.etaGF = 1e-4