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')

<matplotlib.collections.QuadMesh object at 0x7f626272f3d0>

Or by string concatenation, directly as:

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

<matplotlib.collections.QuadMesh object at 0x7f626273b130>

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  85.3996  59.9  89.9996
92.0000  87.4001  59.0  92.0001
94.0000  89.3999  60.1  93.9999
96.0000  91.4005  58.0  96.0005
98.0000  93.3998  60.4  97.9998
100.0000  95.4006  59.3  100.0006
102.0000  97.4000  58.4  102.0000
104.0000  99.4001  59.4  104.0001
106.0000  101.4004  57.8  106.0004
108.0000  103.4002  59.6  108.0002
110.0000  105.4004  58.6  110.0004
112.0000  107.4000  60.1  112.0000
114.0000  109.3998  59.8  113.9998
116.0000  111.4000  59.2  116.0000
118.0000  113.4004  59.0  118.0004
120.0000  115.3998  59.5  119.9998
122.0000  117.4011  56.9  122.0011
124.0000  119.3998  59.7  123.9998
126.0000  121.4004  58.4  126.0004
128.0000  123.4001  59.7  128.0001
130.0000  125.4004  58.0  130.0004
132.0000  127.4006  58.6  132.0006
134.0000  129.3998  60.7  133.9998
136.0000  131.4001  60.0  136.0001
138.0000  133.3997  59.8  137.9997
140.0000  135.4006  58.7  140.0006
142.0000  137.3998  59.7  141.9998
144.0000  139.4007  57.0  144.0007
146.0000  141.4001  59.2  146.0001
148.0000  143.4010  56.3  148.0010

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)

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hv = 89.99957738107904 eV,  E_F = 85 eV,  Res = 60 meV
hv = 92.00005633215237 eV,  E_F = 87 eV,  Res = 59 meV
hv = 93.9998998647602 eV,  E_F = 89 eV,  Res = 60 meV
hv = 96.00054092254172 eV,  E_F = 91 eV,  Res = 58 meV
hv = 97.99978947421637 eV,  E_F = 93 eV,  Res = 60 meV
hv = 100.00055938890128 eV,  E_F = 95 eV,  Res = 59 meV
hv = 101.99998737501795 eV,  E_F = 97 eV,  Res = 58 meV
hv = 104.00008269025085 eV,  E_F = 99 eV,  Res = 59 meV
hv = 106.00042519683815 eV,  E_F = 101 eV,  Res = 58 meV
hv = 108.00022330501888 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')

<matplotlib.collections.QuadMesh object at 0x7f6262236950>

Plotting iso-energetic cut at ekin = efermi

entry.isoenergy(0).show()

<matplotlib.collections.QuadMesh object at 0x7f62622bb760>

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,
)

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()

<matplotlib.collections.QuadMesh object at 0x7f62622ba5c0>

sphinx_gallery_thumbnail_number = 17

entry.isoenergy(0).show(cmap='cividis')

<matplotlib.collections.QuadMesh object at 0x7f6261fdb370>

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()

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()