Graphene hv scan

Simple workflow for analyzing a photon energy scan data of graphene as simulated from a third nearest neighbor tight binding model. The same workflow can be applied to any photon energy scan.

Import the “fundamental” python libraries for a generic data analysis:

import numpy as np
import matplotlib.pyplot as plt

Instead of loading the file as for example:

# from navarp.utils import navfile
# file_name = r"nxarpes_simulated_cone.nxs"
# entry = navfile.load(file_name)

Here we build the simulated graphene signal with a dedicated function defined just for this purpose:

from navarp.extras.simulation import get_tbgraphene_hv

entry = get_tbgraphene_hv(
    scans=np.arange(90, 150, 2),
    angles=np.linspace(-7, 7, 300),
    ebins=np.linspace(-3.3, 0.4, 450),
    tht_an=-18,
)

Plot a single analyzer image at scan = 90

First I have to extract the isoscan from the entry, so I use the isoscan method of entry:

iso0 = entry.isoscan(scan=90)

Then to plot it using the ‘show’ method of the extracted iso0:

iso0.show(yname='ekin')

Out:

<matplotlib.collections.QuadMesh object at 0x7f88bf18f3d0>

Or by string concatenation, directly as:

entry.isoscan(scan=90).show(yname='ekin')

Out:

<matplotlib.collections.QuadMesh object at 0x7f88bff3cdd0>

Fermi level determination

The initial guess for the binding energy is: ebins = ekins - (hv - work_fun). However, the better way is to proper set the Fermi level first and then derives everything form it. In this case the Fermi level kinetic energy is changing along the scan since it is a photon energy scan. So to set the Fermi level I have to give an array of values corresponding to each photon energy. By definition I can give:

efermis = entry.hv - entry.analyzer.work_fun
entry.set_efermi(efermis)

Or I can use a method for its detection, but in this case, it is important to give a proper energy range for each photon energy. For example for each photon a good range is within 0.4 eV around the photon energy minus the analyzer work function:

energy_range = (
    (entry.hv[:, None] - entry.analyzer.work_fun) +
    np.array([-0.4, 0.4])[None, :])

entry.autoset_efermi(energy_range=energy_range)

Out:

scan(eV)  efermi(eV)  FWHM(meV)  new hv(eV)
90.0000  85.4002  59.1  90.0002
92.0000  87.4002  58.6  92.0002
94.0000  89.3999  59.4  93.9999
96.0000  91.3999  58.3  95.9999
98.0000  93.4010  57.1  98.0010
100.0000  95.4004  59.3  100.0004
102.0000  97.4003  58.6  102.0003
104.0000  99.4007  58.2  104.0007
106.0000  101.4005  58.7  106.0005
108.0000  103.4001  57.8  108.0001
110.0000  105.4000  58.9  110.0000
112.0000  107.4004  59.0  112.0004
114.0000  109.4004  59.4  114.0004
116.0000  111.4007  57.0  116.0007
118.0000  113.4007  58.0  118.0007
120.0000  115.3997  60.7  119.9997
122.0000  117.4001  59.6  122.0001
124.0000  119.4002  58.8  124.0002
126.0000  121.3999  59.4  125.9999
128.0000  123.4003  58.0  128.0003
130.0000  125.4008  57.6  130.0008
132.0000  127.4000  59.0  132.0000
134.0000  129.4007  58.7  134.0007
136.0000  131.4003  58.8  136.0003
138.0000  133.4005  59.1  138.0005
140.0000  135.4001  59.3  140.0001
142.0000  137.3999  60.4  141.9999
144.0000  139.4001  59.1  144.0001
146.0000  141.4004  58.0  146.0004
148.0000  143.3999  59.5  147.9999

In both cases the binding energy and the photon energy will be updated consistently. Note that the work function depends on the beamline or laboratory. If not specified is 4.5 eV.

To check the Fermi level detection I can have a look on each photon energy. Here I show only the first 10 photon energies:

for scan_i in range(10):
    print("hv = {} eV,  E_F = {:.0f} eV,  Res = {:.0f} meV".format(
        entry.hv[scan_i],
        entry.efermi[scan_i],
        entry.efermi_fwhm[scan_i]*1000
    ))
    entry.plt_efermi_fit(scan_i=scan_i)

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Out:

hv = 90.00020111984664 eV,  E_F = 85 eV,  Res = 59 meV
hv = 92.00021531733567 eV,  E_F = 87 eV,  Res = 59 meV
hv = 93.99992288529215 eV,  E_F = 89 eV,  Res = 59 meV
hv = 95.99992708456995 eV,  E_F = 91 eV,  Res = 58 meV
hv = 98.00095379279354 eV,  E_F = 93 eV,  Res = 57 meV
hv = 100.00039070510493 eV,  E_F = 95 eV,  Res = 59 meV
hv = 102.00025876040007 eV,  E_F = 97 eV,  Res = 59 meV
hv = 104.00070771313781 eV,  E_F = 99 eV,  Res = 58 meV
hv = 106.00049817478725 eV,  E_F = 101 eV,  Res = 59 meV
hv = 108.00010710778888 eV,  E_F = 103 eV,  Res = 58 meV

Plot a single analyzer image at scan = 110 with the Fermi level aligned

entry.isoscan(scan=110).show(yname='eef')

Out:

<matplotlib.collections.QuadMesh object at 0x7f88bf974810>

Plotting iso-energetic cut at ekin = efermi

entry.isoenergy(0).show()

Out:

<matplotlib.collections.QuadMesh object at 0x7f88bf95e250>

Plotting in the reciprocal space (k-space)

I have to define first the reference point to be used for the transformation. Meaning a point in the angular space which I know it correspond to a particular point in the k-space. In this case the graphene Dirac-point is for hv = 120 is at ekin = 114.3 eV and tht_p = -0.6 (see the figure below), which in the k-space has to correspond to kx = 1.7.

hv_p = 120

entry.isoscan(scan=hv_p, dscan=0).show(yname='ekin', cmap='cividis')

tht_p = -0.6
e_kin_p = 114.3
plt.axvline(tht_p, color='w')
plt.axhline(e_kin_p, color='w')

entry.set_kspace(
    tht_p=tht_p,
    k_along_slit_p=1.7,
    scan_p=0,
    ks_p=0,
    e_kin_p=e_kin_p,
    inn_pot=14,
    p_hv=True,
    hv_p=hv_p,
)

Out:

tht_an = -18.040
scan_type =  hv
inn_pot = 14.000
phi_an = 0.000
k_perp_slit_for_kz = 0.000
kspace transformation ready

Once it is set, all the isoscan or iscoenergy extracted from the entry will now get their proper k-space scales:

entry.isoscan(120).show()

Out:

<matplotlib.collections.QuadMesh object at 0x7f88bfe65590>

sphinx_gallery_thumbnail_number = 17

entry.isoenergy(0).show(cmap='cividis')

Out:

<matplotlib.collections.QuadMesh object at 0x7f88bf9f5950>

I can also place together in a single figure different images:

fig, axs = plt.subplots(1, 2)

entry.isoscan(120).show(ax=axs[0])
entry.isoenergy(-0.9).show(ax=axs[1])

plt.tight_layout()

Many other options:

fig, axs = plt.subplots(2, 2)

scan = 110
dscan = 0
ebin = -0.9
debin = 0.01

entry.isoscan(scan, dscan).show(ax=axs[0][0], xname='tht', yname='ekin')
entry.isoscan(scan, dscan).show(ax=axs[0][1], cmap='binary')

axs[0][1].axhline(ebin-debin)
axs[0][1].axhline(ebin+debin)

entry.isoenergy(ebin, debin).show(
    ax=axs[1][0], xname='tht', yname='phi', cmap='cividis')
entry.isoenergy(ebin, debin).show(
    ax=axs[1][1], cmap='magma', cmapscale='log')

axs[1][0].axhline(scan, color='w', ls='--')
axs[0][1].axvline(1.7, color='r', ls='--')
axs[1][1].axvline(1.7, color='r', ls='--')

x_note = 0.05
y_note = 0.98

for ax in axs[0][:]:
    ax.annotate(
        "$scan \: = \: {} eV$".format(scan, dscan),
        (x_note, y_note),
        xycoords='axes fraction',
        size=8, rotation=0, ha="left", va="top",
        bbox=dict(
            boxstyle="round", fc='w', alpha=0.65, edgecolor='None', pad=0.05
        )
    )

for ax in axs[1][:]:
    ax.annotate(
        "$E-E_F \: = \: {} \pm {} \; eV$".format(ebin, debin),
        (x_note, y_note),
        xycoords='axes fraction',
        size=8, rotation=0, ha="left", va="top",
        bbox=dict(
            boxstyle="round", fc='w', alpha=0.65, edgecolor='None', pad=0.05
        )
    )

plt.tight_layout()