calculateVelocity¶

calculateVelocity(configuration, kpoint=None, spin=None, band_indices=None)

Calculates the Bloch-state velocity $$\frac{1}{\hbar} \frac{dE}{dk}$$ using first order perturbation theory.

Parameters: configuration (BulkConfiguration) – The configuration for which to calculate the velocity. kpoint (tuple of floats) – The kpoint as three floats representing fractional reciprocal space coordinates. Default: The Gamma point (0.0, 0.0, 0.0) spin (Spin.Up | Spin.Down | Spin.All) – The spin component for which to perform the calculation. Default: Spin.All band_indices (list of non-negative int) – Indices of the bands for which to calculate the velocity. Default: All bands (range(number_of_bands)) The velocities for each band. numpy.array

Usage Examples¶

Evaluate the valence band velocity for graphene at the Dirac point:

# -------------------------------------------------------------
# Bulk configuration
# -------------------------------------------------------------

# Set up configuration
bulk_configuration = BulkConfiguration(
bravais_lattice=Hexagonal(2.4612*Angstrom, 6.709*Angstrom),
elements=[Carbon, Carbon],
fractional_coordinates=[[ 0.333333333333,  0.166666666667,  0.5 ],
[ 0.666666666667,  0.833333333333,  0.5 ]],
)

# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------
calculator = LCAOCalculator()

bulk_configuration.setCalculator(calculator)
nlprint(bulk_configuration)
bulk_configuration.update()

# Fractional k-point, slighly displaced away from the Dirac point.
k = [1./3+0.001, 1./3+0.001, 0  ]

# Calculate the velocity of the band with band-index 3 (valence band)
velocity = calculateVelocity(bulk_configuration, kpoint=k, spin=Spin.Up, band_indices=)
# Take the velocity component along the X cartesian direction.
velocity = velocity

# Print the result.
print('Fermi velocity of graphene:')
print('v = %.2e m/s' %abs(velocity.inUnitsOf(Meter/Second)))


graphene_velocity.py

Running the script you will get a Fermi velocity of $$v_F=8.4\cdot 10^{5}$$ m/s, which is close to literature values, genereally reported to be $$\approx 10^6$$ m/s.