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 0x7f145fae86e0>

Or by string concatenation, directly as:

entry.isoscan(scan=90).show(yname='ekin')
plot gr hv scan
<matplotlib.collections.QuadMesh object at 0x7f145f1e1400>

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  85.3998  59.2  89.9998
92.0000  87.4002  57.7  92.0002
94.0000  89.4001  59.0  94.0001
96.0000  91.4005  58.6  96.0005
98.0000  93.4002  59.4  98.0002
100.0000  95.3997  59.9  99.9997
102.0000  97.4007  57.2  102.0007
104.0000  99.4004  58.8  104.0004
106.0000  101.4004  57.8  106.0004
108.0000  103.4010  57.6  108.0010
110.0000  105.4000  59.6  110.0000
112.0000  107.4004  58.9  112.0004
114.0000  109.4004  58.4  114.0004
116.0000  111.4006  57.6  116.0006
118.0000  113.4004  58.9  118.0004
120.0000  115.4000  59.9  120.0000
122.0000  117.4000  59.8  122.0000
124.0000  119.4008  56.8  124.0008
126.0000  121.4001  58.9  126.0001
128.0000  123.4005  59.2  128.0005
130.0000  125.4001  59.0  130.0001
132.0000  127.3999  60.3  131.9999
134.0000  129.4002  59.5  134.0002
136.0000  131.4007  58.5  136.0007
138.0000  133.4001  58.7  138.0001
140.0000  135.4006  59.4  140.0006
142.0000  137.4003  58.9  142.0003
144.0000  139.4005  58.1  144.0005
146.0000  141.4000  59.6  146.0000
148.0000  143.4002  59.0  148.0002

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 = 89.99978970003316 eV,  E_F = 85 eV,  Res = 59 meV
hv = 92.00016898868621 eV,  E_F = 87 eV,  Res = 58 meV
hv = 94.00012594639259 eV,  E_F = 89 eV,  Res = 59 meV
hv = 96.00052873366924 eV,  E_F = 91 eV,  Res = 59 meV
hv = 98.00020348211383 eV,  E_F = 93 eV,  Res = 59 meV
hv = 99.99971289497063 eV,  E_F = 95 eV,  Res = 60 meV
hv = 102.00068252211598 eV,  E_F = 97 eV,  Res = 57 meV
hv = 104.00039004030394 eV,  E_F = 99 eV,  Res = 59 meV
hv = 106.00036964547085 eV,  E_F = 101 eV,  Res = 58 meV
hv = 108.00097458563678 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')
plot gr hv scan
<matplotlib.collections.QuadMesh object at 0x7f145edc5250>

Plotting iso-energetic cut at ekin = efermi

entry.isoenergy(0).show()
plot gr hv scan
<matplotlib.collections.QuadMesh object at 0x7f145ed1fec0>

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 0x7f145ea5ff80>

sphinx_gallery_thumbnail_number = 17

entry.isoenergy(0).show(cmap='cividis')
plot gr hv scan
<matplotlib.collections.QuadMesh object at 0x7f145ea5cef0>

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
/build/reproducible-path/navarp-1.6.0/examples/plot_gr_hv_scan.py:29: SyntaxWarning: invalid escape sequence '\:'
  entry = get_tbgraphene_hv(
/build/reproducible-path/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 4.865 seconds)

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