Transport calculations

One relevant feature of the library is the ability to perform transport calculations of systems using the Landaur-Buttiker formalism. Next we describe how to set up a transport experiment.

Setting up the device

The library only allows to perform two-terminal calculations. Given some material, the first thing to do define the right and left leads. For example, in this case we start from a hydrogen chain to which we append another Bravais vector to describe instead a hydrogen on a square lattice (which could have been done also directly with the configuration file). From it we define a ribbon of a certain width and length. The leads are defined as a motif: they contain the positions of the unit cell of the lead.

from tightbinder.models import SlaterKoster
from tightbinder.fileparse import parse_config_file
from tightbinder.observables import TransportDevice
import numpy as np

length, width = 10, 4

file = open("./examples/chain.txt", "r")
config = parse_config_file(file)
model = SlaterKoster(config)

model.bravais_lattice = np.concatenate((model.bravais_lattice, np.array([[0., 1, 0]])))
model = model.reduce(n2=width)

left_lead = np.copy(model.motif)
left_lead[:, :3] -= model.bravais_lattice[0]

right_lead = np.copy(model.motif)
right_lead[: , :3] += length * model.bravais_lattice[0]

period = model.bravais_lattice[0, 0]

model = model.reduce(n1=length)

Calculation of the transmission

Once the leads and the material are defined, we simply pass them to tightbinder.observables.TransportDevice to create the transport device. Calling tightbinder.observables.TransportDevice.transmission() we compute the transmission on the specified energy range. Note that in the creation of the device one also has to specify the Bravais lattice vector used to define the leads, i.e. the spacing between lead unit cells.

from tightbinder.models import SlaterKoster
from tightbinder.fileparse import parse_config_file
from tightbinder.observables import TransportDevice
import numpy as np

length, width = 10, 4

file = open("./examples/chain.txt", "r")
config = parse_config_file(file)
model = SlaterKoster(config)

model.bravais_lattice = np.concatenate((model.bravais_lattice, np.array([[0., 1, 0]])))
model = model.reduce(n2=width)

left_lead = np.copy(model.motif)
left_lead[:, :3] -= model.bravais_lattice[0]

right_lead = np.copy(model.motif)
right_lead[: , :3] += length * model.bravais_lattice[0]

period = model.bravais_lattice[0, 0]

model = model.reduce(n1=length)

device = TransportDevice(model, left_lead, right_lead, period, "default")
trans, energy = device.transmission(-5, 5, 300)

Conductance

Alternatively, we can compute directly the conductance of the system at \(T=0\), namely the transmission at the Fermi energy. This can be done with the tightbinder.observables.TransportDevice.conductance() method.

from tightbinder.models import SlaterKoster
from tightbinder.fileparse import parse_config_file
from tightbinder.observables import TransportDevice
import numpy as np

length, width = 10, 4

file = open("./examples/chain.txt", "r")
config = parse_config_file(file)
model = SlaterKoster(config)

model.bravais_lattice = np.concatenate((model.bravais_lattice, np.array([[0., 1, 0]])))
model = model.reduce(n2=width)

left_lead = np.copy(model.motif)
left_lead[:, :3] -= model.bravais_lattice[0]

right_lead = np.copy(model.motif)
right_lead[: , :3] += length * model.bravais_lattice[0]

period = model.bravais_lattice[0, 0]

model = model.reduce(n1=length)

device = TransportDevice(model, left_lead, right_lead, period, "default")
G = device.conductance()

Visualizing the device

Finally, it is also useful to plot the transport device to ensure that both the leads, the central sample and the bonds between all of them are correct. This can be done calling the tightbinder.observables.TransportDevice.visualize_device() method.

from tightbinder.models import SlaterKoster
from tightbinder.fileparse import parse_config_file
from tightbinder.observables import TransportDevice
import numpy as np
import matplotlib.pyplot as plt

length, width = 10, 4

file = open("./examples/chain.txt", "r")
config = parse_config_file(file)
model = SlaterKoster(config)

model.bravais_lattice = np.concatenate((model.bravais_lattice, np.array([[0., 1, 0]])))
model = model.reduce(n2=width)

left_lead = np.copy(model.motif)
left_lead[:, :3] -= model.bravais_lattice[0]

right_lead = np.copy(model.motif)
right_lead[: , :3] += length * model.bravais_lattice[0]

period = model.bravais_lattice[0, 0]

model = model.reduce(n1=length)

device = TransportDevice(model, left_lead, right_lead, period, "default")
device.visualize_device()

plt.show()