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')
plot gr hv scan

Out:

<matplotlib.collections.QuadMesh object at 0x7f91f9d54210>

Or by string concatenation, directly as:

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f91f9e72790>

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  85.3999  59.9  89.9999
92.0000  87.3998  58.5  91.9998
94.0000  89.3994  60.7  93.9994
96.0000  91.4004  57.8  96.0004
98.0000  93.4004  59.3  98.0004
100.0000  95.4001  59.3  100.0001
102.0000  97.4002  58.8  102.0002
104.0000  99.4005  58.7  104.0005
106.0000  101.4010  57.5  106.0010
108.0000  103.3997  59.9  107.9997
110.0000  105.4001  59.4  110.0001
112.0000  107.4007  58.4  112.0007
114.0000  109.4005  58.1  114.0005
116.0000  111.4002  59.4  116.0002
118.0000  113.4008  57.4  118.0008
120.0000  115.4009  57.6  120.0009
122.0000  117.4000  60.0  122.0000
124.0000  119.4000  60.3  124.0000
126.0000  121.3998  59.0  125.9998
128.0000  123.4006  58.6  128.0006
130.0000  125.3997  59.9  129.9997
132.0000  127.4000  59.7  132.0000
134.0000  129.4003  59.0  134.0003
136.0000  131.4002  58.5  136.0002
138.0000  133.4004  58.6  138.0004
140.0000  135.4003  59.2  140.0003
142.0000  137.4004  58.8  142.0004
144.0000  139.4000  59.1  144.0000
146.0000  141.3998  60.2  145.9998
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)
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan

Out:

hv = 89.9998738611425 eV,  E_F = 85 eV,  Res = 60 meV
hv = 91.99976715674832 eV,  E_F = 87 eV,  Res = 59 meV
hv = 93.99939401430593 eV,  E_F = 89 eV,  Res = 61 meV
hv = 96.0003924997328 eV,  E_F = 91 eV,  Res = 58 meV
hv = 98.00038148538293 eV,  E_F = 93 eV,  Res = 59 meV
hv = 100.00007864343151 eV,  E_F = 95 eV,  Res = 59 meV
hv = 102.00022919963484 eV,  E_F = 97 eV,  Res = 59 meV
hv = 104.0004864784704 eV,  E_F = 99 eV,  Res = 59 meV
hv = 106.00102622412413 eV,  E_F = 101 eV,  Res = 58 meV
hv = 107.99970039300567 eV,  E_F = 103 eV,  Res = 60 meV

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

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f91f9975d50>

Plotting iso-energetic cut at ekin = efermi

entry.isoenergy(0).show()
plot gr hv scan

Out:

<matplotlib.collections.QuadMesh object at 0x7f91f986f910>

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,
)
plot gr hv scan

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()
plot gr hv scan

Out:

<matplotlib.collections.QuadMesh object at 0x7f91f95d14d0>

sphinx_gallery_thumbnail_number = 17

entry.isoenergy(0).show(cmap='cividis')
plot gr hv scan

Out:

<matplotlib.collections.QuadMesh object at 0x7f91f9658550>

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()
plot gr hv scan

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()
plot gr hv scan

Total running time of the script: ( 0 minutes 3.782 seconds)

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