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from __future__ import print_function
import sisl
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

TranSiesta allows a great variety of contours when performing the equilibrium contours

In this example you will try and create different contours for the equilibrium part.

The default contours are defined like this:

%block TS.ChemPot.Left
  mu V/2
  contour.eq
    begin
      C-Left
      T-Left
    end
%endblock TS.ChemPot.Left
%block TS.ChemPot.Right
  mu -V/2
  contour.eq
    begin
      C-Right
      T-Right
    end
%endblock TS.ChemPot.Right

TS.Contours.Eq.Pole 2.5 eV
%block TS.Contour.C-Left
  part circle
   from -40. eV + V/2 to -10 kT + V/2
     points 25
      method g-legendre
%endblock TS.Contour.C-Left
%block TS.Contour.T-Left
  part tail
   from prev to inf
     points 10
      method g-fermi
%endblock TS.Contour.T-Left
%block TS.Contour.C-Right
  part circle
   from -40. eV -V/2 to -10 kT -V/2
     points 25
      method g-legendre
%endblock TS.Contour.C-Right
%block TS.Contour.T-Right
  part tail
   from prev to inf
     points 10
      method g-fermi
%endblock TS.Contour.T-Right

Add a temperature gradient

The default temperatures of the chemical potentials are the Siesta electronic temperature. TranSiesta enables to distinguish the electrodes by their chemical potential and their electronic temperature. I.e. the distribution functions of the electrodes may be very different:



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def nf(E, mu, kT):
    return 1 / (1 + np.exp( (E-mu) / kT ))
# Generate two different distributions
E = np.linspace(-2, 2, 100)
plt.plot(E, nf(E, 0.25, 0.025), label='V=0.25, kT=0.025');
plt.plot(E, nf(E, -0.25, 0.05), label='V=-0.25, kT=0.05');
plt.plot(E, nf(E, 0.25, 0.025) - nf(E, -0.25, 0.05), '.', label=r'$\delta n_F$');
plt.legend();

When implementing this in the input-options it will likely fail if one of the electrodes has a temperature higher than the TS.ElectronicTemperature (defaults to ElectronicTemperature). This is because TranSiesta will fail if one of the tail integrals in the non-equilibrium contour is not at least 5 kT from the respective chemical potential, hence correct the non-equilibrium contour input.

Reduce number of equilibrium contours

Instead of using 2 contours per chemical potential one can reduce it to 2 contours (in total). I.e. the chemical potentials shares the same contours. Note however, in this case one cannot use the Gauss-Fermi quadrature for the tail part of the complex contour. Hence choose something different than g-fermi.

Copy TS 02 and adapt the contours such that there are only 2 contours regardless of the applied bias. When testing various contours, you can add TS.Analyze to the input to make it quite after the analyzation step. This will also be after the corresponding siesta.TSCCEQ* files are created.

You can use the following line to read in the contour data-points:

CC = sisl.io.tableSile('<>/siesta.TSCCEQ-Left').read_data()

where CC is a matrix variable with 4 rows:

`CC[0, :]`	`CC[1, :]`	`CC[2, :]`	`CC[3, :]`
Real energy	Imaginary energy	Real weight	Imaginary weight



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