Is ATK able to reproduce the experimental IV curve for bulk gold?

[gst]

I'm still deciding if I should purchase ATK or not. As one of the tests I'm trying to reproduce the experimental conductivity of simple metals.

I have been trying without success to reproduce the experimental IV curve for gold. Invariably, the calculates conductivity is more than 10 times smaller than the experimental one, ~4.5E7 S/m. I would expect it to be higher, since the system is defect free and single crystal.

Have anyone had success reproducing the experimental conductivity of simple metals? If so please tell me the recipe.

I used the script below:

# -------------------------------------------------------------
# TwoProbe configuration
# -------------------------------------------------------------

# -------------------------------------------------------------
# Left electrode
# -------------------------------------------------------------

# Set up lattice
vector_a = [5.02259, 0.0, 0.0]*Angstrom
vector_b = [1.79916535203e-16, 2.93826, 0.0]*Angstrom
vector_c = [0.0, 0.0, 14.77686]*Angstrom
left_electrode_lattice = UnitCell(vector_a, vector_b, vector_c)

# Define elements
left_electrode_elements = [Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold,
                           Gold, Gold]

# Define coordinates
left_electrode_coordinates = [[  0.41676981,   0.7345657 ,   1.23139213],
                              [  2.92806367,   2.20369422,   1.23139396],
                              [  1.25573221,   2.2036943 ,   3.69415997],
                              [  3.76683931,   0.7345657 ,   3.69426439],
                              [  2.09471311,   0.7345657 ,   6.15693373],
                              [  4.60582019,   2.20369429,   6.15703787],
                              [  0.41676981,   0.7345657 ,   8.61982213],
                              [  2.92806367,   2.20369422,   8.61982396],
                              [  1.25573221,   2.2036943 ,  11.08258997],
                              [  3.76683931,   0.7345657 ,  11.08269439],
                              [  2.09471311,   0.7345657 ,  13.54536373],
                              [  4.60582019,   2.20369429,  13.54546787]]*Angstrom

# Set up configuration
left_electrode = BulkConfiguration(
    bravais_lattice=left_electrode_lattice,
    elements=left_electrode_elements,
    cartesian_coordinates=left_electrode_coordinates
    )

# -------------------------------------------------------------
# Right electrode
# -------------------------------------------------------------

# Set up lattice
vector_a = [5.02259, 0.0, 0.0]*Angstrom
vector_b = [1.79916535203e-16, 2.93826, 0.0]*Angstrom
vector_c = [0.0, 0.0, 14.77686]*Angstrom
right_electrode_lattice = UnitCell(vector_a, vector_b, vector_c)

# Define elements
right_electrode_elements = [Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold,
                            Gold, Gold]

# Define coordinates
right_electrode_coordinates = [[  0.41676981,   0.7345657 ,   1.23139213],
                               [  2.92806367,   2.20369422,   1.23139396],
                               [  1.25573221,   2.2036943 ,   3.69415997],
                               [  3.76683931,   0.7345657 ,   3.69426439],
                               [  2.09471311,   0.7345657 ,   6.15693373],
                               [  4.60582019,   2.20369429,   6.15703787],
                               [  0.41676981,   0.7345657 ,   8.61982213],
                               [  2.92806367,   2.20369422,   8.61982396],
                               [  1.25573221,   2.2036943 ,  11.08258997],
                               [  3.76683931,   0.7345657 ,  11.08269439],
                               [  2.09471311,   0.7345657 ,  13.54536373],
                               [  4.60582019,   2.20369429,  13.54546787]]*Angstrom

# Set up configuration
right_electrode = BulkConfiguration(
    bravais_lattice=right_electrode_lattice,
    elements=right_electrode_elements,
    cartesian_coordinates=right_electrode_coordinates
    )

# -------------------------------------------------------------
# Central region
# -------------------------------------------------------------

# Set up lattice
vector_a = [5.02259, 0.0, 0.0]*Angstrom
vector_b = [1.79916535203e-16, 2.93826, 0.0]*Angstrom
vector_c = [2.26205428756e-15, 2.26205428756e-15, 36.94215]*Angstrom
central_region_lattice = UnitCell(vector_a, vector_b, vector_c)

# Define elements
central_region_elements = [Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold,
                           Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold,
                           Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold, Gold]

# Define coordinates
central_region_coordinates = [[  0.41676981,   0.7345657 ,   1.23139213],
                              [  2.92806367,   2.20369422,   1.23139396],
                              [  1.25573221,   2.2036943 ,   3.69415997],
                              [  3.76683931,   0.7345657 ,   3.69426439],
                              [  2.09471311,   0.7345657 ,   6.15693373],
                              [  4.60582019,   2.20369429,   6.15703787],
                              [  0.41676981,   0.7345657 ,   8.61982213],
                              [  2.92806367,   2.20369422,   8.61982396],
                              [  1.25573221,   2.2036943 ,  11.08258997],
                              [  3.76683931,   0.7345657 ,  11.08269439],
                              [  2.09471311,   0.7345657 ,  13.54536373],
                              [  4.60582019,   2.20369429,  13.54546787],
                              [  0.41676981,   0.7345657 ,  16.00825213],
                              [  2.92806367,   2.20369422,  16.00825396],
                              [  1.25573221,   2.2036943 ,  18.47101997],
                              [  3.76683931,   0.7345657 ,  18.47112439],
                              [  2.09471311,   0.7345657 ,  20.93379373],
                              [  4.60582019,   2.20369429,  20.93389787],
                              [  0.41676981,   0.7345657 ,  23.39668213],
                              [  2.92806367,   2.20369422,  23.39668396],
                              [  1.25573221,   2.2036943 ,  25.85944997],
                              [  3.76683931,   0.7345657 ,  25.85955439],
                              [  2.09471311,   0.7345657 ,  28.32222373],
                              [  4.60582019,   2.20369429,  28.32232787],
                              [  0.41676981,   0.7345657 ,  30.78511213],
                              [  2.92806367,   2.20369422,  30.78511396],
                              [  1.25573221,   2.2036943 ,  33.24787997],
                              [  3.76683931,   0.7345657 ,  33.24798439],
                              [  2.09471311,   0.7345657 ,  35.71065373],
                              [  4.60582019,   2.20369429,  35.71075787]]*Angstrom

# Set up configuration
central_region = BulkConfiguration(
    bravais_lattice=central_region_lattice,
    elements=central_region_elements,
    cartesian_coordinates=central_region_coordinates
    )

device_configuration = DeviceConfiguration(
    central_region,
    [left_electrode, right_electrode]
    )
nlprint(device_configuration)

# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------
#----------------------------------------
# Basis Set
#----------------------------------------
basis_set = GGABasis.DoubleZetaPolarized

#----------------------------------------
# Exchange-Correlation
#----------------------------------------
exchange_correlation = GGA.PBE

#----------------------------------------
# Numerical Accuracy Settings
#----------------------------------------
left_electrode_numerical_accuracy_parameters = NumericalAccuracyParameters(
    k_point_sampling=(3, 5, 150),
    )

right_electrode_numerical_accuracy_parameters = NumericalAccuracyParameters(
    k_point_sampling=(3, 5, 150),
    )

device_numerical_accuracy_parameters = NumericalAccuracyParameters(
    k_point_sampling=(3, 5, 1),
    )

#----------------------------------------
# Iteration Control Settings
#----------------------------------------
device_iteration_control_parameters = IterationControlParameters(
    tolerance=1e-07,
    )

#----------------------------------------
# Poisson Solver Settings
#----------------------------------------
left_electrode_poisson_solver = FastFourier2DSolver(
    boundary_conditions=[[PeriodicBoundaryCondition,PeriodicBoundaryCondition],
                         [PeriodicBoundaryCondition,PeriodicBoundaryCondition],
                         [PeriodicBoundaryCondition,PeriodicBoundaryCondition]]
    )

right_electrode_poisson_solver = FastFourier2DSolver(
    boundary_conditions=[[PeriodicBoundaryCondition,PeriodicBoundaryCondition],
                         [PeriodicBoundaryCondition,PeriodicBoundaryCondition],
                         [PeriodicBoundaryCondition,PeriodicBoundaryCondition]]
    )

#----------------------------------------
# Electrode Calculators
#----------------------------------------
left_electrode_calculator = LCAOCalculator(
    basis_set=basis_set,
    exchange_correlation=exchange_correlation,
    numerical_accuracy_parameters=left_electrode_numerical_accuracy_parameters,
    poisson_solver=left_electrode_poisson_solver,
    )

right_electrode_calculator = LCAOCalculator(
    basis_set=basis_set,
    exchange_correlation=exchange_correlation,
    numerical_accuracy_parameters=right_electrode_numerical_accuracy_parameters,
    poisson_solver=right_electrode_poisson_solver,
    )


# Define output NetCDF file
scf_filename = 'Au-bulk_iv_scf_analysis-GGA2.nc'

#----------------------------------------
# Device Calculator
#----------------------------------------
calculator = DeviceLCAOCalculator(
    basis_set=basis_set,
    exchange_correlation=exchange_correlation,
    numerical_accuracy_parameters=device_numerical_accuracy_parameters,
    iteration_control_parameters=device_iteration_control_parameters,
    electrode_calculators=
        [left_electrode_calculator, right_electrode_calculator],
    )

nlprint(device_configuration)
for voltage in [0., 0.1, 0.2, 0.3, 0.4, 0.5]*Volt:
    device_configuration.setCalculator(
        calculator(electrode_voltages=(-0.5*voltage,0.5*voltage)),
        initial_state=device_configuration
    )
    device_configuration.update()
    nlsave(scf_filename, device_configuration)

#
# Calculate the transmission spectra
#

# Define output NetCDF file
analysis_filename = 'Au-bulk_iv_scf_analysis-GGA2.nc'

# -------------------------------------------------------------
# Transmission spectrum
# -------------------------------------------------------------

# Read all self-consistent calculations from NetCDF file
configurations = nlread(scf_filename, DeviceConfiguration)

for configuration in configurations:

    # For each one, extract the bias,
    calculator = configuration.calculator()
    bias = calculator.electrodeVoltages()[1]-calculator.electrodeVoltages()[0]

    # ... calculate and save the transmission spectrum,
    transmission_spectrum = TransmissionSpectrum(
        configuration=configuration,
        energies=numpy.linspace(-2,2,101)*eV,
        kpoints=MonkhorstPackGrid(9,15),
        energy_zero_parameter=AverageFermiLevel,
        infinitesimal=1e-06*eV,
        self_energy_calculator=KrylovSelfEnergy(),
    )   
    nlsave(analysis_filename, transmission_spectrum, object_id="Transmission %s" % bias)
   
    potential = EffectivePotential(configuration)
    # Calculate and save the voltage drop (except for zero bias, of course)
    if float(bias)!=0.:
        voltage_drop = potential - zero_bias_potential
        nlsave(analysis_filename, voltage_drop, object_id="Voltage drop %s" % bias)
    else:
        zero_bias_potential = potential
       
# Copy geometry to analysis file, for plotting
zero_bias_calculation = nlread(scf_filename, DeviceConfiguration, read_state = False)[0]
nlsave(analysis_filename, zero_bias_calculation)

[nori]

Is ATK able to reproduce the experimental IV curve for bulk gold?

No, it isn't because ATK treats coherent transport properties of nano-scale system, which is lost in macro-scale.
So transport properties calculated with ATK don't obey ohm's law.
In your case, the transport is ballistic and the conductance does not depend on the length of the central region.

[gst]

I see!!! Make all sense. Actually, just for fun I tested, and the IV curve does not change at all making the central region twice as large. That makes me wonder if it make sense to use ATK to calculate IV curves for an amorphous bulk system. Can it handle incoherent transport in an amorphous nano-scale material? 

[nori]

Can it handle incoherent transport in an amorphous nano-scale material?

Unfortunately at least current version of ATK only supports coherent transport.
If you requests incoherent transport to QuantumWise staff, it may be on the road map for future release

[Anders Blom]

Indeed, incoherent and inelastic transport is currently not available, and in general it's a very difficult (and not least extremely time-consuming) calculation to perform.

It's important to understand the basic premises for a two-probe calculation. It's tempting to use a perfect system as a test, but actually that is the one case where the algorithm breaks down. For the transport approach implemented in ATK (and any similar transport code) is based on the concept that somewhere inside the simulation region there is a resistive part where the voltage difference between the two electrodes can be off-loaded.

Thus a perfect metallic system cannot be simulated - but then again you don't need to, you know the answer. It's ballistic conductance is G0 per mode at each energy. What's interesting - and possible - it to simulate a system where you cannot predict the answer, because of scattering, imperfections, a junction between a metal and a semiconductor, etc, and this is where ATK can help. Just as long as it's not a perfect conductor

That said, also a perfect semiconductor would not really work. But a short piece of semiconductor between two metal leads, for sure.

For a pure material, it would actually be much more reasonably to do a completely different calculation than to set up a whole transport system. By computing the complex band structure along a direction of interest, you can judge at least the difference in (ballistic) conductance between different materials, or different directions if the material is anisotropic. The functionality to compute the complex band structure is available in ATK since 11.2, and the algorithm has been improved a bit in 11.8.

Hope this helps, otherwise let us how we can further assist you.