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 0x7f750c6c03d0>

Or by string concatenation, directly as:

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f750c62be80>

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  85.3998  59.4  89.9998
92.0000  87.4002  58.9  92.0002
94.0000  89.4001  58.1  94.0001
96.0000  91.4001  59.1  96.0001
98.0000  93.4002  59.1  98.0002
100.0000  95.4000  59.0  100.0000
102.0000  97.4004  58.4  102.0004
104.0000  99.4009  57.4  104.0009
106.0000  101.4003  58.4  106.0003
108.0000  103.4003  58.4  108.0003
110.0000  105.4003  59.6  110.0003
112.0000  107.4004  59.2  112.0004
114.0000  109.4002  58.5  114.0002
116.0000  111.4004  58.4  116.0004
118.0000  113.4004  58.7  118.0004
120.0000  115.4006  58.1  120.0006
122.0000  117.4005  58.1  122.0005
124.0000  119.4000  58.9  124.0000
126.0000  121.4006  58.5  126.0006
128.0000  123.4007  57.9  128.0007
130.0000  125.4000  59.8  130.0000
132.0000  127.4003  58.9  132.0003
134.0000  129.3997  60.2  133.9997
136.0000  131.4004  58.7  136.0004
138.0000  133.4003  59.0  138.0003
140.0000  135.3997  60.8  139.9997
142.0000  137.4002  59.5  142.0002
144.0000  139.4000  58.7  144.0000
146.0000  141.4006  57.8  146.0006
148.0000  143.4002  59.2  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

Out:

hv = 89.99983261915811 eV,  E_F = 85 eV,  Res = 59 meV
hv = 92.00024905844872 eV,  E_F = 87 eV,  Res = 59 meV
hv = 94.00008301988478 eV,  E_F = 89 eV,  Res = 58 meV
hv = 96.0001286240135 eV,  E_F = 91 eV,  Res = 59 meV
hv = 98.00019431692235 eV,  E_F = 93 eV,  Res = 59 meV
hv = 100.00001779788433 eV,  E_F = 95 eV,  Res = 59 meV
hv = 102.00044424253366 eV,  E_F = 97 eV,  Res = 58 meV
hv = 104.0009166329101 eV,  E_F = 99 eV,  Res = 57 meV
hv = 106.00031664427812 eV,  E_F = 101 eV,  Res = 58 meV
hv = 108.0002899714147 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

Out:

<matplotlib.collections.QuadMesh object at 0x7f750c0e0100>

Plotting iso-energetic cut at ekin = efermi

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f750c621f70>

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 0x7f750c3d25e0>

sphinx_gallery_thumbnail_number = 17

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

Out:

<matplotlib.collections.QuadMesh object at 0x7f750c422580>

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 4.843 seconds)

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