Intercalated graphene
In this example, we extract the self-energies and Eliashberg function of Si-intercalated, Li-doped graphene.
Data have been provided with permission for re-use, originating from: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.085132
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%load_ext autoreload
%autoreload 2
# Necessary packages
import xarpes
import matplotlib.pyplot as plt
import os
# Default plot configuration from xarpes.plotting.py
xarpes.plot_settings('default')
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script_dir = xarpes.set_script_dir()
dfld = 'data_sets' # Folder containing the data
flnm = 'graphene_152' # Name of the file
extn = '.ibw' # Extension of the file
data_file_path = os.path.join(script_dir, dfld, flnm + extn)
The following cell instantiates band map class object based on the Igor Binary Wave (ibw) file. The subsequent cell illustrates how a band map object could be instantiated with NumPy arrays instead. Only one of the cells will have to be executed to populate the band map object.
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%matplotlib inline
bmap = xarpes.BandMap.from_ibw_file(data_file_path, energy_resolution=0.01,
angle_resolution=0.1, temperature=50)
bmap.shift_angles(shift=-2.28)
fig = bmap.plot(abscissa='momentum', ordinate='kinetic_energy', size_kwargs=dict(w=6, h=5))
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# %matplotlib inline
# import numpy as np
# intensities= np.load(os.path.join(script_dir, dfld, "graphene_152_intensities.npy"))
# angles = np.load(os.path.join(script_dir, dfld, "graphene_152_angles.npy"))
# ekin = np.load(os.path.join(script_dir, dfld, "graphene_152_ekin.npy"))
# bmap = xarpes.BandMap.from_np_arrays(intensities=intensities, angles=angles,
# ekin=ekin, energy_resolution=0.01, angle_resolution=0.1,temperature=50)
# fig = bmap.plot(abscissa='momentum', ordinate='kinetic_energy', size_kwargs=dict(w=6, h=5))
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%matplotlib inline
fig, ax = plt.subplots(2, 1, figsize=(6, 8))
bmap.correct_fermi_edge(
hnuminPhi_guess=32, background_guess=1e2,
integrated_weight_guess=1e3, angle_min=-10, angle_max=10,
ekin_min=31.96, ekin_max=32.08, true_angle=0.0,
ax=ax[0], show=False, fig_close=False)
bmap.plot(ordinate='electron_energy', abscissa='momentum',
ax=ax[1], show=False, fig_close=False)
# Figure customization
ax[0].set_xlabel(''); ax[0].set_xticklabels([])
ax[0].set_title('Fermi correction fit')
fig.subplots_adjust(top=0.92, hspace=0.1)
plt.show()
print('The optimised hnu - Phi=' + f'{bmap.hnuminPhi:.4f}' + ' +/- '
+ f'{1.96 * bmap.hnuminPhi_std:.5f}' + ' eV.')
# fig = bmap.plot(ordinate='kinetic_energy', abscissa='angle')
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%matplotlib inline
fig = bmap.fit_fermi_edge(hnuminPhi_guess=32, background_guess=1e5,
integrated_weight_guess=1.5e6, angle_min=-10,
angle_max=20, ekin_min=31.96, ekin_max=32.08,
show=True, title='Fermi edge fit')
print('The optimised hnu - Phi=' + f'{bmap.hnuminPhi:.4f}' + ' +/- '
+ f'{1.96 * bmap.hnuminPhi_std:.5f}' + ' eV.')
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%matplotlib inline
angle_min = -11.5
angle_max = 11.5
energy_range = [-0.246, 0.01]
energy_value = 0.0
mdcs = xarpes.MDCs(*bmap.mdc_set(angle_min, angle_max, energy_range=energy_range))
guess_dists = xarpes.CreateDistributions([
xarpes.Linear(offset=3.0e3, slope=-100),
xarpes.SpectralLinear(amplitude=1.5e3, peak=-6.9, broadening=0.015,
name='Linear_left', index='1'),
xarpes.SpectralLinear(amplitude=1.3e3, peak=7.1, broadening=0.015,
name='Linear_right', index='2')
])
k_diff = -0.13
import numpy as np
# Eq. S13 of the supplemental information.
# Currently E_kin cannot be supplied as an argument, so it is fixed to hnuminPhi
mat_el = lambda x: (1 + k_diff / np.sqrt(k_diff ** 2 + bmap.hnuminPhi *
np.sin(np.deg2rad(x)) ** 2 / xarpes.PREF))
mat_args = {}
fig = plt.figure(figsize=(8, 6)); ax = fig.gca()
fig = mdcs.visualize_guess(distributions=guess_dists, energy_value=energy_value,
matrix_element=mat_el, matrix_args=mat_args, ax=ax)
Note on interactive figures
The interactive figure might not work inside the Jupyter notebooks, despite our best efforts to ensure stability.
As a fallback, the user may switch from “%matplotlib widget” to “%matplotlib qt”, after which the figure should pop up in an external window.
For some package versions, a static version of the interactive widget may spuriously show up inside other cells. In that case, uncomment the #get_ipython()… line in the first cell for your notebooks.
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%matplotlib widget
fig = plt.figure(figsize=(8, 6))
ax = fig.gca()
mdcs = xarpes.MDCs(*bmap.mdc_set(angle_min, angle_max, energy_range=energy_range))
fig = mdcs.fit_selection(distributions=guess_dists,
matrix_element=mat_el, matrix_args=mat_args, ax=ax)
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%matplotlib inline
plt.rcParams['lines.markersize'] = 0.8
fig = plt.figure(figsize=(8, 6)); ax = fig.gca()
self_energy = xarpes.SelfEnergy(*mdcs.expose_parameters(select_label='Linear_right_2',
fermi_velocity=2.851291959, fermi_wavevector=0.357807))
self_energies = xarpes.CreateSelfEnergies([self_energy])
fig = bmap.plot(abscissa='momentum', ordinate='electron_energy', ax=ax,
self_energies=self_energies)
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%matplotlib inline
fig, spectrum, model, omega_range, aval_select = self_energy.extract_a2f(
omega_min=0.5, omega_max=250, omega_num=250, omega_I=50, omega_M=200,
omega_S=1, aval_min=1.0, aval_max=9.0, aval_num=10, method="chi2kink",
parts="both", ecut_left=0.0, ecut_right=None, t_criterion=1e-8,
sigma_svd=1e-4, iter_max=1e4, lambda_el=0.0, W=1500, h_n=0.1062861,
impurity_magnitude=120.94606, power=4, f_chi_squared=None)
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%matplotlib inline
fig = plt.figure(figsize=(6, 5)); ax = fig.gca()
fig = self_energy.plot_spectra(ax=ax)
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with xarpes.trim_notebook_output(print_lines=10):
spectrum, model, omega_range, aval_select, cost, params = self_energy.bayesian_loop(omega_min=0.5,
omega_max=250, omega_num=250, omega_I=50, omega_M=200, omega_S=1.0,
W=1500, power=4, fermi_velocity=2.8590436, fermi_wavevector=0.358010499,
h_n=0.0802309738, impurity_magnitude=120.902261, lambda_el=0,
vary=("impurity_magnitude", "lambda_el", "fermi_wavevector", "fermi_velocity", "h_n"),
converge_iters=10, tole=1e-2, scale_vF=1.0, scale_imp=1.0, scale_kF=0.1,
scale_lambda_el=1.0, scale_hn=10.0)
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%matplotlib inline
angle_min2 = -1e6
angle_max2 = 0
plt.rcParams['lines.markersize'] = 3.0
mdc2 = xarpes.MDCs(*bmap.mdc_set(angle_min2, angle_max2, energy_range=energy_range))
guess_dists2 = xarpes.CreateDistributions([
xarpes.Linear(offset=2.0e3, slope=100),
xarpes.SpectralLinear(amplitude=450, peak=-7.25, broadening=0.01,
name='Linear_left', index='1'),
])
fig = plt.figure(figsize=(8, 6)); ax = fig.gca()
fig = mdc2.visualize_guess(distributions=guess_dists2, energy_value=0, ax=ax)
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# Fit without showing output
fig = mdc2.fit_selection(distributions=guess_dists2, show=False, fig_close=True)
self_left = xarpes.SelfEnergy(*mdc2.expose_parameters(select_label='Linear_left_1',
fermi_velocity=-2.67, fermi_wavevector=-0.354))
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%matplotlib inline
fig = plt.figure(figsize=(8, 5)); ax = fig.gca()
self_energies= xarpes.CreateSelfEnergies([
self_energy, self_left
])
fig = bmap.plot(abscissa='momentum', ordinate='electron_energy',
self_energies=self_energies, plot_dispersions='full',
ax=ax)
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%matplotlib inline
fig = plt.figure(figsize=(8, 6)); ax = fig.gca()
self_left.plot_both(ax=ax, show=False, fig_close=False)
self_energy.plot_both(ax=ax, show=False, fig_close=False)
ax.set_xlim([-0.275, 0.025])
ax.set_ylim([-0.025, 0.275])
plt.legend(); plt.show()
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%matplotlib inline
fig = plt.figure(figsize=(8, 6)); ax = fig.gca()
self_left.plot_both(ax=ax, show=False, fig_close=False)
self_energy.plot_both(ax=ax, show=False, fig_close=False)
ax.set_xlim([-0.275, 0.025]); ax.set_ylim([-0.025, 0.275])
# Replace labels with custom labels
left_real, left_imag, right_real, right_imag = ax.get_lines()
labels = [
r"$\Sigma_{\mathrm{L}}'(E)$", r"$-\Sigma_{\mathrm{L}}''(E)$",
r"$\Sigma_{\mathrm{R}}'(E)$", r"$-\Sigma_{\mathrm{R}}''(E)$",
]
ax.legend([left_real, left_imag, right_real, right_imag], labels)
plt.show()
