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 0x7fc17f508a70>

Or by string concatenation, directly as:

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

Out:

<matplotlib.collections.QuadMesh object at 0x7fc17f4235c0>

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  85.3994  59.0  89.9994
92.0000  87.4003  58.5  92.0003
94.0000  89.4001  58.1  94.0001
96.0000  91.4002  59.5  96.0002
98.0000  93.4003  58.7  98.0003
100.0000  95.4001  58.3  100.0001
102.0000  97.4001  60.3  102.0001
104.0000  99.4002  58.9  104.0002
106.0000  101.4006  57.7  106.0006
108.0000  103.3998  59.5  107.9998
110.0000  105.4003  58.5  110.0003
112.0000  107.4005  58.2  112.0005
114.0000  109.4005  57.7  114.0005
116.0000  111.4004  58.1  116.0004
118.0000  113.4000  59.5  118.0000
120.0000  115.4004  58.3  120.0004
122.0000  117.4006  59.0  122.0006
124.0000  119.4003  58.1  124.0003
126.0000  121.4013  57.6  126.0013
128.0000  123.4001  59.2  128.0001
130.0000  125.4004  58.6  130.0004
132.0000  127.4001  59.2  132.0001
134.0000  129.4004  57.8  134.0004
136.0000  131.4000  58.9  136.0000
138.0000  133.4002  58.2  138.0002
140.0000  135.4000  59.6  140.0000
142.0000  137.4005  57.7  142.0005
144.0000  139.4002  60.0  144.0002
146.0000  141.4000  60.0  146.0000
148.0000  143.4004  57.8  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

Out:

hv = 89.99942834431931 eV,  E_F = 85 eV,  Res = 59 meV
hv = 92.00026887225881 eV,  E_F = 87 eV,  Res = 58 meV
hv = 94.00010029054313 eV,  E_F = 89 eV,  Res = 58 meV
hv = 96.00023377048528 eV,  E_F = 91 eV,  Res = 59 meV
hv = 98.0002856355874 eV,  E_F = 93 eV,  Res = 59 meV
hv = 100.00010646840092 eV,  E_F = 95 eV,  Res = 58 meV
hv = 102.00009783714764 eV,  E_F = 97 eV,  Res = 60 meV
hv = 104.00019832573207 eV,  E_F = 99 eV,  Res = 59 meV
hv = 106.00060016300287 eV,  E_F = 101 eV,  Res = 58 meV
hv = 107.99982757096905 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 0x7fc17f10f2f0>

Plotting iso-energetic cut at ekin = efermi

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

Out:

<matplotlib.collections.QuadMesh object at 0x7fc17f2d30e0>

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 0x7fc17f000500>

sphinx_gallery_thumbnail_number = 17

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

Out:

<matplotlib.collections.QuadMesh object at 0x7fc17eef34a0>

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

Out:

/build/navarp-ZUoQIo/navarp-1.6.0/examples/plot_gr_hv_scan.py:29: SyntaxWarning: invalid escape sequence '\:'
  entry = get_tbgraphene_hv(
/build/navarp-ZUoQIo/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 5.308 seconds)

Gallery generated by Sphinx-Gallery