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
<matplotlib.collections.QuadMesh object at 0x7904007df890>

Or by string concatenation, directly as:

entry.isoscan(scan=90).show(yname='ekin')
plot gr hv scan
<matplotlib.collections.QuadMesh object at 0x7903ffd429c0>

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)
scan(eV)  efermi(eV)  FWHM(meV)  new hv(eV)
90.0000  85.3999  58.9  89.9999
92.0000  87.3999  59.8  91.9999
94.0000  89.3996  60.3  93.9996
96.0000  91.3994  59.8  95.9994
98.0000  93.4000  59.8  98.0000
100.0000  95.4009  58.3  100.0009
102.0000  97.4003  59.0  102.0003
104.0000  99.4004  58.8  104.0004
106.0000  101.3999  58.4  105.9999
108.0000  103.4001  59.1  108.0001
110.0000  105.4000  59.4  110.0000
112.0000  107.4003  57.4  112.0003
114.0000  109.4005  58.5  114.0005
116.0000  111.3996  59.4  115.9996
118.0000  113.4007  58.2  118.0007
120.0000  115.4000  60.6  120.0000
122.0000  117.4009  57.8  122.0009
124.0000  119.4001  58.9  124.0001
126.0000  121.4009  56.8  126.0009
128.0000  123.4005  58.6  128.0005
130.0000  125.4000  59.7  130.0000
132.0000  127.4001  58.2  132.0001
134.0000  129.4002  59.6  134.0002
136.0000  131.4008  58.1  136.0008
138.0000  133.4009  57.3  138.0009
140.0000  135.4005  58.4  140.0005
142.0000  137.3998  60.4  141.9998
144.0000  139.4004  58.7  144.0004
146.0000  141.4002  59.8  146.0002
148.0000  143.4004  58.4  148.0004

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
hv = 89.99987021446691 eV,  E_F = 85 eV,  Res = 59 meV
hv = 91.99993757671932 eV,  E_F = 87 eV,  Res = 60 meV
hv = 93.99958077616644 eV,  E_F = 89 eV,  Res = 60 meV
hv = 95.99936286034557 eV,  E_F = 91 eV,  Res = 60 meV
hv = 98.0000077076337 eV,  E_F = 93 eV,  Res = 60 meV
hv = 100.00089427679168 eV,  E_F = 95 eV,  Res = 58 meV
hv = 102.00032650103083 eV,  E_F = 97 eV,  Res = 59 meV
hv = 104.00040248890004 eV,  E_F = 99 eV,  Res = 59 meV
hv = 105.9999013504625 eV,  E_F = 101 eV,  Res = 58 meV
hv = 108.00007668122778 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
<matplotlib.collections.QuadMesh object at 0x7903ffcab8c0>

Plotting iso-energetic cut at ekin = efermi

entry.isoenergy(0).show()
plot gr hv scan
<matplotlib.collections.QuadMesh object at 0x7903ffa2a2d0>

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
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
<matplotlib.collections.QuadMesh object at 0x7903ffa2ac90>

sphinx_gallery_thumbnail_number = 17

entry.isoenergy(0).show(cmap='cividis')
plot gr hv scan
<matplotlib.collections.QuadMesh object at 0x7903ff916ba0>

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
/workspace/repo-tools/run-upstream-build/navarp-1.6.0/examples/plot_gr_hv_scan.py:29: SyntaxWarning: invalid escape sequence '\:'
  entry = get_tbgraphene_hv(
/workspace/repo-tools/run-upstream-build/navarp-1.6.0/examples/plot_gr_hv_scan.py:40: SyntaxWarning: invalid escape sequence '\:'
  # method of entry:

Total running time of the script: (0 minutes 2.158 seconds)

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