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 0x7f068ddae0a0>

Or by string concatenation, directly as:

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f068dd871c0>

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  85.4005  58.3  90.0005
92.0000  87.3999  59.3  91.9999
94.0000  89.4006  57.7  94.0006
96.0000  91.4002  59.8  96.0002
98.0000  93.4002  59.3  98.0002
100.0000  95.3996  59.7  99.9996
102.0000  97.4008  56.7  102.0008
104.0000  99.4007  59.6  104.0007
106.0000  101.4008  57.9  106.0008
108.0000  103.4002  58.9  108.0002
110.0000  105.4004  58.1  110.0004
112.0000  107.3996  60.4  111.9996
114.0000  109.3998  59.9  113.9998
116.0000  111.4001  59.0  116.0001
118.0000  113.3999  58.9  117.9999
120.0000  115.4006  57.8  120.0006
122.0000  117.4002  59.9  122.0002
124.0000  119.4000  59.3  124.0000
126.0000  121.3996  60.1  125.9996
128.0000  123.4001  59.4  128.0001
130.0000  125.4006  58.4  130.0006
132.0000  127.4008  58.3  132.0008
134.0000  129.3997  60.9  133.9997
136.0000  131.4005  58.6  136.0005
138.0000  133.4003  58.9  138.0003
140.0000  135.4004  58.5  140.0004
142.0000  137.4004  58.6  142.0004
144.0000  139.4005  57.9  144.0005
146.0000  141.4001  59.1  146.0001
148.0000  143.4006  58.1  148.0006

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
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  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan
  • plot gr hv scan

Out:

hv = 90.00049742385123 eV,  E_F = 85 eV,  Res = 58 meV
hv = 91.99990331519464 eV,  E_F = 87 eV,  Res = 59 meV
hv = 94.00057487742069 eV,  E_F = 89 eV,  Res = 58 meV
hv = 96.0002003239522 eV,  E_F = 91 eV,  Res = 60 meV
hv = 98.00016513582878 eV,  E_F = 93 eV,  Res = 59 meV
hv = 99.99956872726189 eV,  E_F = 95 eV,  Res = 60 meV
hv = 102.00081477901384 eV,  E_F = 97 eV,  Res = 57 meV
hv = 104.00067479598724 eV,  E_F = 99 eV,  Res = 60 meV
hv = 106.0008095560272 eV,  E_F = 101 eV,  Res = 58 meV
hv = 108.00022009795744 eV,  E_F = 103 eV,  Res = 59 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 0x7f068dd48760>

Plotting iso-energetic cut at ekin = efermi

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f068de92a30>

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 0x7f068dfcfa90>

sphinx_gallery_thumbnail_number = 17

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f068dfd6d30>

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 5.766 seconds)

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