SelfEnergies

File containing the band map class.

class xarpes.selfenergies.SelfEnergy(ekin_range, hnuminPhi, energy_resolution, temperature, label, properties, parameters)

Self-energy

property energy_resolution

Energy resolution associated with the self-energy.

property temperature

Temperature associated with the self-energy [K].

property parameters

Dictionary with user-supplied parameters (read-only view).

property side

Optional side selector: ‘left’ or ‘right’.

property fermi_wavevector

Optional k_F; can be set later.

property fermi_velocity

Optional v_F; can be set later.

property bare_mass

Optional bare mass; used by SpectralQuadratic formulas.

property center_wavevector

Read-only center wavevector (SpectralQuadratic, if present).

property peak_positions

k_parallel = peak * dtor * sqrt(ekin_range / PREF) (lazy).

property peak_positions_sigma

Std. dev. of k_parallel (lazy).

property imag

-Σ’’ (lazy).

property imag_sigma

Std. dev. of -Σ’’ (lazy).

property real

Σ’ (lazy).

property real_sigma

Std. dev. of Σ’ (lazy).

property a2f_spectrum

Cached α²F(ω) spectrum from last extraction (or None).

property a2f_model

Cached MEM model spectrum from last extraction (or None).

property a2f_omega_range

Cached ω grid for the last extraction (or None).

property a2f_aval_select

Cached selected a-value from last extraction (or None).

property a2f_cost

Cached cost from last bayesian_loop (or None).

property reconstructed_real_ph

Phonon-only reconstructed real part from latest MEM run (or None).

property reconstructed_imag_ph

Phonon-only reconstructed imaginary part from latest MEM run (or None).

property reconstructed_real

Reconstructed real part with e-e contribution added back.

property reconstructed_imag

Reconstructed imaginary part with e-e and impurity terms added back.

property reconstructed_real_el

Electron-electron contribution to reconstructed real part.

property reconstructed_imag_el

Electron-electron contribution to reconstructed imaginary part.

property reconstructed_imag_imp

Impurity contribution vector for reconstructed imaginary part.

property ecut_left

Cached left energy cutoff (meV) from the latest MEM run.

property ecut_right

Cached right energy cutoff (meV) from the latest MEM run.

None means the algorithms used self.energy_resolution as right cutoff.

property mdc_maxima

MDC maxima (lazy).

SpectralLinear:

identical to peak_positions

SpectralQuadratic:

peak_positions + center_wavevector

plot_real(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot the real part Σ’ of the self-energy as a function of E-μ.

Parameters:

axMatplotlib-Axes or None

Axis to plot on. Created if not provided by the user.

scale{“eV”, “meV”}

Units for both axes. If “meV”, x and y (and yerr) are multiplied by KILO.

resolution_range{“absent”, “applied”}

If “applied”, applies the same energy mask used by extract_a2f/bayesian_loop based on cached ecut_left/ecut_right values.

**kwargs

Additional keyword arguments passed to ax.errorbar.

Returns:

figMatplotlib-Figure

Figure containing the Σ’(E) plot.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_imag(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot the imaginary part -Σ’’ of the self-energy vs. E-μ.

Parameters:

axMatplotlib-Axes or None

Axis to plot on. Created if not provided by the user.

scale{“eV”, “meV”}

Units for both axes. If “meV”, x and y (and yerr) are multiplied by KILO.

resolution_range{“absent”, “applied”}

If “applied”, applies the same energy mask used by extract_a2f/bayesian_loop based on cached ecut_left/ecut_right values.

**kwargs

Additional keyword arguments passed to ax.errorbar.

Returns:

figMatplotlib-Figure

Figure containing the -Σ’’(E) plot.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_both(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot Σ’(E) and -Σ’’(E) vs. E-μ on the same axis.

Parameters:

axMatplotlib-Axes or None

Axis to plot on. Created if not provided by the user.

scale{“eV”, “meV”}

Units for both axes. If “meV”, x, y, and yerr are multiplied by KILO.

resolution_range{“absent”, “applied”}

If “applied”, applies the same energy mask used by extract_a2f/bayesian_loop based on cached ecut_left/ecut_right values.

**kwargs

Additional keyword arguments passed to ax.errorbar.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_real(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed Σ’(E) vs. E-μ from the latest MEM workflow.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_imag(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed -Σ’’(E) vs. E-μ from the latest MEM workflow.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_both(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed Σ’(E) and -Σ’’(E) vs. E-μ on the same axis.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_real_ph(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed phonon contribution Σ_ph(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_imag_ph(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed phonon contribution -Σ’’_ph(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_both_ph(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed phonon Σ’(E) and -Σ’’(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_real_el(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed electron contribution Σ_el(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_imag_el(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed electron contribution -Σ’’_el(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_both_el(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed electron Σ’(E) and -Σ’’(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_real_imp(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed impurity real contribution Σ_imp(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_imag_imp(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed impurity imaginary contribution -Σ’’_imp(E).

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_reconstructed_both_imp(ax=None, scale='eV', resolution_range='absent', **kwargs)

Plot reconstructed impurity Σ’(E) and -Σ’’(E) vs. E-μ.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_a2f(ax=None, abscissa='forward', **kwargs)

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_model(ax=None, abscissa='forward', **kwargs)

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

plot_spectra(ax=None, abscissa='forward', **kwargs)

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

extract_a2f(*, omega_min, omega_max, omega_num, omega_I, omega_M, ax=None, method=None, parts=None, iter_max=None, aval_min=None, aval_max=None, aval_num=None, ecut_left=None, ecut_right=None, f_chi_squared=None, W=None, power=None, mu=None, omega_S=None, sigma_svd=None, t_criterion=None, g_guess=None, b_guess=None, c_guess=None, d_guess=None, h_n=None, h_n_min=None, impurity_magnitude=None, lambda_el=None)

Extract Eliashberg function α²F(ω) from the self-energy. While working with band maps and MDCs is more intuitive in eV, the self-energy extraction is performed in eV.

Parameters:

axMatplotlib-Axes or None

Axis to plot on. Created if not provided by the user. (Not used yet; reserved for future plotting.)

method{“chi2kink”}

MEM selection method.

parts{“both”, “real”, “imag”}

Which part of the self-energy to fit.

iter_maxint

Maximum number of MEM iterations.

aval_min, aval_maxfloat

Minimum and maximum a values scanned in the chi2kink procedure.

aval_numint

Number of a values scanned.

ecut_leftfloat

Left energy cutoff in meV, measured upward from the lowest energy.

ecut_rightfloat or None

Right energy cutoff in meV below the chemical potential. If None, self.energy_resolution is used.

f_chi_squaredfloat or None

Target chi-squared threshold factor. If None, defaults to 2.5 for parts='both' and 2.0 otherwise.

Wfloat or None

Electron-electron interaction scale in meV, required when lambda_el is nonzero for linearised bands.

powerint

Power used in the electron-electron self-energy model.

mufloat

MEM regularisation parameter.

omega_Sfloat

Switch-on scale for the model function.

sigma_svdfloat

Singular-value cutoff used in the SVD.

t_criterionfloat

Convergence criterion for chi2kink.

g_guess, b_guess, c_guess, d_guessfloat

Initial guesses for the chi2kink logistic fit.

h_nfloat or None

Model normalisation parameter. Must be provided.

impurity_magnitudefloat

Constant impurity contribution subtracted from -Σ’’.

lambda_elfloat

Strength of the electron-electron self-energy contribution.

Returns:

figMatplotlib-Figure

Figure showing the chi2kink selection curve.

spectrumndarray

Extracted α²F(ω).

modelndarray

MEM model spectrum.

omega_rangendarray

ω grid used for the extraction.

aval_selectfloat

Selected a-value returned by the chi2kink procedure.

Notes

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: True.

bayesian_loop(*, omega_min, omega_max, omega_num, omega_I, omega_M, fermi_velocity=None, fermi_wavevector=None, bare_mass=None, vary=(), opt_method='Nelder-Mead', opt_options=None, method=None, parts=None, iter_max=None, aval_min=None, aval_max=None, aval_num=None, ecut_left=None, ecut_right=None, f_chi_squared=None, W=None, power=None, mu=None, omega_S=None, sigma_svd=None, t_criterion=None, g_guess=None, b_guess=None, c_guess=None, d_guess=None, h_n=None, h_n_min=None, impurity_magnitude=None, lambda_el=None, converge_iters=None, tole=None, scale_vF=None, scale_mb=None, scale_imp=None, scale_kF=None, scale_lambda_el=None, scale_hn=None, opt_iter_max=None, rollback_steps=None, max_retries=None, relative_best=None, min_steps_for_regression=None)

Bayesian outer loop calling _cost_function().

If vary is non-empty, runs a SciPy optimization over the selected parameters in vary.

Supported entries in vary depend on self._class:

• Common: “fermi_wavevector”, “impurity_magnitude”, “lambda_el”, “h_n”

• SpectralLinear: additionally “fermi_velocity”

• SpectralQuadratic: additionally “bare_mass”

Parameters:

opt_optionsdict, optional

Options passed directly to scipy.optimize.minimize. These are only used for convergence if the custom criterion is disabled (see Notes).

Notes

Convergence behaviour

By default, convergence is controlled by a custom patience criterion: the optimization terminates when the absolute difference between the current cost and the best cost seen so far is smaller than tole for converge_iters consecutive iterations.

To instead rely on SciPy’s native convergence criteria (e.g. Nelder–Mead xatol / fatol), disable the custom criterion by setting converge_iters=0 or tole=None. In that case, SciPy termination options supplied via opt_options are used.

class xarpes.selfenergies.CreateSelfEnergies(self_energies)

Thin container for self-energies with leaf-aware utilities. All items are assumed to be leaf self-energy objects with a .label attribute for identification.

get_by_label(label)

Return the self-energy object with the given label.

Parameters:

labelstr

Label of the self-energy to retrieve.

Returns:

objSelfEnergy

The corresponding self-energy instance.

Raises:

KeyError

If no self-energy with the given label exists.

labels()

Return a list of all labels.

as_dict()

Return a {label: self_energy} dictionary for convenient access.