Advanced Examples

This section provides advanced examples demonstrating specialized features of gauNEGF.

Spin Transport

Example of spin-dependent transport:

from gauNEGF.scf import NEGF
from gauNEGF.transport import cohTransSpin

# Initialize with unrestricted calculation
negf = NEGF(
    fn='molecule',
    spin='u'  # Unrestricted calculation
)

# Set up spin-dependent contacts
sig_up = [-0.1j]
sig_down = [-0.05j]
inds = negf.setSigma([1], [2])
sig1 = np.diag(sig_up*len(inds[0]) + sig_down*len(inds[0]))
sig2 = np.diag(sig_down*len(inds[1]) + sig_up*len(inds[1]))
negf.setSigma([1], [2], sig1, sig2)

# Run at equilibrium
negf.setVoltage(0.0)
negf.SCF(1e-3, 0.01)

# Calculate spin-resolved transmission
sigma1, sigma1 = negf.getSigma()
T, Tspin = cohTransSpin(
    E, negf.F, negf.S,
    sigma1, sigma2,
    spin='u'
)

Temperature Effects

Including finite temperature:

# Set basic temperature-dependent contact
negf.setSigma(
    [1], [2],
    -0.05j,
    T=300     # Temperature in Kelvin
)

# Set up temperature-dependent Bethe Lattice contacts
negf.setContactBethe(
    contactList=[[1,2,3], [4,5,6]],
    latFile='Au',
    T=300  # Temperature in Kelvin
)

Energy-Dependent Contacts

Using realistic contact models:

# Bethe lattice contacts at atoms {1,2,3} and {6,7,8}
negf.setContactBethe(
    contactList=[[1,2,3], [6,7,8]],
    latFile='Au', # Slater coster parameters define in Au.bethe
    eta=1e-6      # Broadening term (eV)
)

# 1D chain contacts attached to atoms 1 and 6
negf.setContact1D(
    contactList= [[1],[6]],
    tauList = [[2], [5]],   # hopping calculated from 1 to 2 and 6 to 5
    neList = [4,  4],       # 4 electrons per cell
    eta = 1e-6              # Broadening term (eV)
)

Parallel Processing

If you know what you are doing and want to parallelize each integration point then you can manually set this in the densityComplex function:

from gauNEGF.density import densityComplex

# Parallel density calculation
P = densityComplex(
    F, S, g,
    Emin=-50,
    mu=0,
    N=100,
    parallel=True,
    numWorkers=4
)

Note this is usually slower than the default numpy parallelization. Only proceed if you know what you are doing

Custom Analysis

Advanced analysis tools:

import numpy as np
import matplotlib.pyplot as plt
from gauNEGF.transport import DOS, cohTransE

#... run energy dependent NEGFE() calculation

# Calculate DOS and transmission
E = np.linspace(-5, 5, 1000)
dos, dos_list = DOSE(E, negf.F, negf.S, g)
T = cohTransE(E, negf.F, negf.S, negf.g)

# Plot correlation
plt.figure(figsize=(10, 5))
plt.subplot(121)
plt.plot(E, dos)
plt.xlabel('Energy (eV)')
plt.ylabel('DOS')

plt.subplot(122)
plt.semilogy(E, T)
plt.xlabel('Energy (eV)')
plt.ylabel('Transmission')

plt.tight_layout()
plt.show()

Next Steps

  1. Develop custom contact models

  2. Implement new analysis tools

  3. Optimize performance

  4. Add error handling