tbplas.Analyzer

class tbplas.Analyzer(sample: Sample, config: Config, dimension: int = 3, enable_mpi: bool = False, echo_details: bool = False)

Class for analyzing correlation functions.

_sample

sample for which TBPM calculations will be performed

Type:

‘Sample’ instance

_config

parameters controlling TBPM calculation

Type:

‘Config’ instance

_dimension

dimension of the system

Type:

int

__init__(sample: Sample, config: Config, dimension: int = 3, enable_mpi: bool = False, echo_details: bool = False) → None

Parameters:

• sample – sample for which TBPM calculations will be performed

• config – parameters controlling TBPM calculations

• dimension – dimension of the sample

• enable_mpi – whether to enable parallelism using MPI

• echo_details – whether to output parallelization details

Raises:

ValueError – if dimension is neither 2 nor 3, or if illegal parameters are detected in config

Methods

__init__(sample, config[, dimension, ...])	param sample: sample for which TBPM calculations will be performed
all_average(data_local)	Average results over random samples broadcast to all process.
all_reduce(data_local)	Reduce local data and broadcast to all processes.
average(data_local)	Average results over random samples and store results to master process.
barrier()	Wrapper for self.comm.Barrier.
bcast(data_local)	Broadcast data from master to other processes.
calc_ac_cond(corr_ac[, window])	Calculate optical (AC) conductivity from correlation function.
calc_dc_cond(corr_dos, corr_dc[, ...])	Calculate electronic (DC) conductivity at zero temperature from its correlation function.
calc_diff_coeff(corr_dc[, window_dc])	Calculate diffusion coefficient form DC correlation function.
calc_dos(corr_dos[, window])	Calculate DOS from correlation function.
calc_dyn_pol(corr_dyn_pol[, window])	Calculate dynamical polarization from correlation function.
calc_epsilon(dyn_pol)	Calculate dielectric function from dynamical polarization.
calc_epsilon_q0(omegas, ac_cond)	Calculate dielectric function from AC conductivity for q=0.
calc_hall_cond(mu_mn[, unit])	Calculate Hall conductivity according to Kubo-Bastin formula mu_mn.
calc_ldos(corr_ldos[, window])	Calculate LDOS from correlation function.
dist_bound(n_max)	Same as dist_range, but returns the lower and upper bounds.
dist_list(raw_list[, algorithm])	Distribute a list over processes.
dist_range(n_max)	Distribute range(n_max) over processes.
log([event, fmt])	Log the date and time of event.
print([text])	Print text on master process.
reduce(data_local)	Reduce local data to master process.

Attributes

is_master	Determine whether this is the master process.
mpi_enabled	Determine whether MPI is enabled.
rank	Interface for the '__rank' attribute.
size	Interface for the '__size' attribute.

__init__(sample: Sample, config: Config, dimension: int = 3, enable_mpi: bool = False, echo_details: bool = False) → None

Parameters:

• sample – sample for which TBPM calculations will be performed

• config – parameters controlling TBPM calculations

• dimension – dimension of the sample

• enable_mpi – whether to enable parallelism using MPI

• echo_details – whether to output parallelization details

Raises:

ValueError – if dimension is neither 2 nor 3, or if illegal parameters are detected in config

all_average(data_local: ndarray) → ndarray

Average results over random samples broadcast to all process.

Parameters:

data_local – local results on each process

Returns:

averaged data from data_local

all_reduce(data_local: ndarray) → ndarray

Reduce local data and broadcast to all processes.

Parameters:

data_local – local results on each process

Returns:

summed data from data_local

average(data_local: ndarray) → ndarray

Average results over random samples and store results to master process.

Parameters:

data_local – local results on each process

Returns:

averaged data from data_local

barrier() → None

Wrapper for self.comm.Barrier.

bcast(data_local: ndarray) → None

Broadcast data from master to other processes.

Parameters:

data_local – local results on each process

Returns:

None

calc_ac_cond(corr_ac: ~numpy.ndarray, window: ~typing.Callable = <function window_exp>) → Tuple[ndarray, ndarray]

Calculate optical (AC) conductivity from correlation function.

Reference: eqn. 300-301 of graphene note.

The unit of AC conductivity in 2d case follows: [sigma] = [1/(h_bar * omega * A)] * [j^2] * [dt]

= 1/(eV*nm^2) * e^2/h_bar^2 * (eV)^2 * nm^2 * h_bar/eV = e^2/h_bar

which is consistent with the results from Lindhard function.

The reason for nr_orbitals in the prefactor is that every electron contribute freely to the conductivity, and we have to take the number of electrons into consideration. See eqn. 222-223 of the note for more details.

Parameters:

• corr_ac – (4, nr_time_steps) complex128 array AC correlation function in 4 directions: xx, xy, yx, yy, respectively Unit should be e^2/h_bar^2 * (eV)^2 * nm^2.

• window – window function for integral

Returns:

(omegas, ac_cond) omegas: (nr_time_steps,) float64 array frequencies in eV ac_cond: (4, nr_time_steps) complex128 array ac conductivity values corresponding to omegas for 4 directions (xx, xy, yx, yy, respectively) The unit is e^2/(h_bar*nm) in 3d case and e^2/h_bar in 2d case.

calc_dc_cond(corr_dos: ~numpy.ndarray, corr_dc: ~numpy.ndarray, window_dos: ~typing.Callable = <function window_hanning>, window_dc: ~typing.Callable = <function window_exp>) → Tuple[ndarray, ndarray]

Calculate electronic (DC) conductivity at zero temperature from its correlation function.

Reference: eqn. 381 of graphene note.

The unit of DC conductivity in 2d case follows: [sigma] = [D/A] * [j^2] * [dt]

= 1/(eV*nm^2) * e^2/h_bar^2 * (eV)^2 * nm^2 * h_bar/eV = e^2/h_bar

which is consistent with the result of Lindhard function.

NOTE: the xy and yx components of conductivity are not accurate. So they will not be evaluated.

NOTE: Here we need to call analyze_corr_dos to obtain DOS, which is intended to analyze the result of calc_corr_dos by design. As in the fortran extension, the results of calc_corr_dos and calc_corr_ldos have the length of nr_time_steps+1, while that of calc_corr_dc has length of nr_time_steps. This is due to incomplete update of the source code. tbpm_dos and tbpm_ldos have been update, while other subroutines are not. So here we need to insert 1.0 to the head of corr_dos by calc_corr_dc before calling analyze_corr_dos.

Parameters:

• corr_dos – (nr_time_steps,) complex128 array dimensionless DOS correlation function

• corr_dc – (2, n_energies, nr_time_steps) complex128 array DC conductivity correlation function in e^2/h_bar^2 * (eV)^2 * nm^2

• window_dos – window function for DOS integral

• window_dc – window function for DC integral

Returns:

(energies, dc) energies: (n_energies,) float64 array energies in eV dc: (2, n_energies) float64 array dc conductivity values for xx and yy directions in the same unit as ac conductivity

calc_diff_coeff(corr_dc: ~numpy.ndarray, window_dc: ~typing.Callable = <function window_exp>) → Tuple[ndarray, ndarray]

Calculate diffusion coefficient form DC correlation function.

Reference: eqn. 43-44 of feature article.

The unit of diff_coeff follows: [diff_coeff] = [1/e^2] * [j^2] * [dt]

= 1/e^2 * e^2/h_bar^2 * (eV)^2 * nm^2 * h_bar/eV = eV*nm^2/h_bar

which does not depend on system dimension.

Parameters:

• corr_dc – (2, n_energies, nr_time_steps) complex128 array DC conductivity correlation function in e^2/h_bar^2 * (eV)^2 * nm^2

• window_dc – window function for DC integral

Returns:

(time, diff_coeff) time: (nr_time_steps,) float64 array time for diffusion coefficient in h_bar/eV diff_coeff: (2, n_energies, nr_time_steps) complex128 array diffusion coefficient in nm^2/(h_bar/eV)

calc_dos(corr_dos: ~numpy.ndarray, window: ~typing.Callable = <function window_hanning>) → Tuple[ndarray, ndarray]

Calculate DOS from correlation function.

Reference: eqn. 16-17 of feature article.

The unit of dos follows:

[dos] = [C_DOS] [dt] = h_bar / eV

So possibly the formula misses a h_bar on the denominator. Anyway, the DOS is correct since it is explicitly normalized to 1.

Parameters:

• corr_dos – (nr_time_steps+1,) complex128 array dimensionless DOS correlation function

• window – window function for integral

Returns:

(energies, dos) energies: (2*nr_time_steps,) float64 array energies in eV dos: (2*nr_time_steps,) float64 array DOS in 1/eV

calc_dyn_pol(corr_dyn_pol: ~numpy.ndarray, window: ~typing.Callable = <function window_exp_ten>) → Tuple[ndarray, ndarray, ndarray]

Calculate dynamical polarization from correlation function.

Reference: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.84.035439

The unit of dp in 2d case follows: [dp] = [1/A] * [C_DP] * [dt]

= 1/nm^2 * 1 * h_bar/eV = h_bar/(eV*nm^2)

which is inconsistent with the output of Lindhard! So, possibly the formula misses a h_bar on the denominator.

Parameters:

• corr_dyn_pol – (n_q_points, nr_time_steps) float64 array dimensionless dynamical polarization correlation function

• window – window function for integral

Returns:

(q_points, omegas, dyn_pol) q_points: (n_q_points, 3) float64 array Cartesian coordinates of q-points in 1/nm omegas: (nr_time_steps,) float64 array frequencies in eV dyn_pol: (n_q_points, nr_time_steps) complex128 array dynamical polarization values corresponding to q-points and omegas The unit is 1/(eV*nm^2) or 1/(eV*nm^3) depending on the dimension.

calc_epsilon(dyn_pol: ndarray) → ndarray

Calculate dielectric function from dynamical polarization.

Parameters:

dyn_pol – (n_q_points, nr_time_steps) complex128 array dynamical polarization

Returns:

(n_q_points, nr_time_steps) complex128 array dielectric function

calc_epsilon_q0(omegas: ndarray, ac_cond: ndarray) → ndarray

Calculate dielectric function from AC conductivity for q=0.

Parameters:

• omegas – (nr_time_steps,) float64 array energies in eV

• ac_cond – (4, nr_time_steps) complex128 array AC conductivity in e**2/(h_bar*nm) in 3d case

Returns:

(4, nr_time_steps,) complex128 array relative dielectric function

Raises:

ValueError – if dimension is not 3

calc_hall_cond(mu_mn: ndarray, unit: str = 'h_bar') → Tuple[ndarray, ndarray]

Calculate Hall conductivity according to Kubo-Bastin formula mu_mn.

Reference: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.116602

The unit of hall_cond in 2d case from eqn. 1 of the reference follows: [hall_cond] = [h_bar*e^2/Omega] * [dE * Tr<…>]

= h_bar*e^2/nm^2 * 1/eV * nm^2/h_bar^2 * eV = e^2/h_bar

which is consistent with AC and DC conductivity. Note that the delta function in the formula has the unit of 1/eV.

The unit can also be determined from enq. 4 as: [hall_cond] = [e^2*h_bar/(Omega*delaE^2)] * [mu]

= h_bar/(nm^2*V^2) * nm^2 * (eV)^2 / h_bar^2 = e^2/h_bar

Note that the scaled energy is dimensionless.

Parameters:

• mu_mn – (n_kernel, n_kernel) complex128 array output of solver.calc_hall_mu in nm^2/h_bar^2 * (eV)^2

• unit – unit of Hall conductivity, set to ‘h_bar’ to use ‘e^2/h_bar’ and ‘h’ to use ‘e^2/h’

Returns:

(energies, conductivity) energies: float64 array chemical potentials specified in config.dckb[‘energies’] conductivity: float64 array Hall conductivity according to energies

Raises:

ValueError – if unit is neither ‘h_bar’ nor ‘h’

calc_ldos(corr_ldos: ~numpy.ndarray, window: ~typing.Callable = <function window_hanning>) → Tuple[ndarray, ndarray]

Calculate LDOS from correlation function.

Parameters:

• corr_ldos – (nr_time_steps+1,) complex128 array dimensionless LDOS correlation function

• window – window function for integral

Returns:

(energies, ldos) energies: (2*nr_time_steps,) float64 array energies in eV ldos: (2*nr_time_steps,) float64 array LDOS in 1/eV

dist_bound(n_max: int) → Tuple[int, int]

Same as dist_range, but returns the lower and upper bounds. Both of the bounds are close, i.e. [i_min, i_max].

Parameters:

n_max – upper bound of range

Returns:

lower and upper bounds of subrange assigned to this process

dist_list(raw_list: List[Any], algorithm: str = 'range') → List[Any]

Distribute a list over processes.

Parameters:

• raw_list – raw list to distribute

• algorithm – distribution algorithm, should be either “remainder” or “range”

Returns:

sublist assigned to this process

dist_range(n_max: int) → range

Distribute range(n_max) over processes.

Parameters:

n_max – upper bound of the range

Returns:

subrange assigned to this process

log(event: str = '', fmt: str = '%x %X') → None

Log the date and time of event.

Parameters:

• event – notice of the event

• fmt – date and time format

Returns:

None.

print(text: str = '') → None

Print text on master process.

NOTE: flush=True is essential for some MPI implementations, e.g. MPICH3.

Parameters:

text – text to print

Returns:

None

reduce(data_local: ndarray) → ndarray

Reduce local data to master process.

Parameters:

data_local – local results on each process

Returns:

summed data from data_local

__weakref__

list of weak references to the object (if defined)

property is_master: bool

Determine whether this is the master process.

property mpi_enabled: bool

Determine whether MPI is enabled.

property rank: int

Interface for the ‘__rank’ attribute.

Returns:

rank of this MPI process

property size: int

Interface for the ‘__size’ attribute.

Returns:

number of MPI processes