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Imaging the Spatial Distribution of Electronic States in Graphene Using
Electron Energy-Loss Spectroscopy: Prospect of Orbital Mapping
M. Bugnet ,1,2,3,* M. Ederer ,4V. K. Lazarov ,5L. Li ,6Q. M. Ramasse ,1,2,7 S. Löffler ,4,†and D. M. Kepaptsoglou 1,5,‡
1SuperSTEM Laboratory, SciTech Daresbury Campus, Daresbury WA4 4AD, United Kingdom
2School of Chemical and Process Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom
3Univ Lyon, CNRS, INSA Lyon, UCBL, MATEIS, UMR 5510, 69621 Villeurbanne, France
4University Service Centre for Transmission Electron Microscopy, TU Wien, Wiedner Hauptstraße 8-10/E057-02, 1040 Wien, Austria
5Department of Physics, University of York, York YO10 5DD, United Kingdom
6Department of Physics and Astronomy, University of West Virginia, Morgantown, West Virginia 26506, USA
7School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
(Received 4 June 2021; revised 23 December 2021; accepted 25 January 2022; published 14 March 2022)
The spatial distributions of antibonding πand σstates in epitaxial graphene multilayers are mapped
using electron energy-loss spectroscopy in a scanning transmission electron microscope. Inelastic
channeling simulations validate the interpretation of the spatially resolved signals in terms of electronic
orbitals, and demonstrate the crucial effect of the material thickness on the experimental capability to
resolve the distribution of unoccupied states. This work illustrates the current potential of core-level
electron energy-loss spectroscopy towards the direct visualization of electronic orbitals in a wide range of
materials, of huge interest to better understand chemical bonding among many other properties at interfaces
and defects in solids.
DOI: 10.1103/PhysRevLett.128.116401
The vast majority of physical and chemical properties of
crystalline materials originates from electronic states gov-
erning chemical bonding. In addition, defects, interfaces,
and surfaces have a direct influence on macroscopic
material properties. Imaging electronic states, such as
chemical bonds at crystal imperfections and discontinuities
in real space, is thus of fundamental and technological
interest to enable the development of new materials with
novel functionalities. While total electronic charge den-
sities have been reconstructed using either electron dif-
fraction [1,2] or high-resolution imaging [3] in the
transmission electron microscope, and more recently
imaged with atomic-scale resolution using four-dimensional
scanning transmission electron microscopy (STEM) [4–6],
the direct observation ofindividual electronic states has been
achieved primarily using scanning tunneling microscopy
[7–10], albeit with surface sensitivity only. Electron energy-
loss spectroscopy (EELS) in an electron microscope is a
spectroscopy technique probing site- and momentum-
projected empty states in the conduction band [11].
Following the development of aberration correctors and
high stability electron optics, atomic resolution EELS in the
scanning transmission electron microscope has become
routinely available, leading to elemental (chemical) mapping
[12–14], and providing real-space atomic scale localization
of electronic states [15–21] using the energy-loss near-edge
structure (ELNES) of the spectroscopic signal.
The ELNES, or spectrum fine structure, arising from
core-level excitation provides a wealth of information on
chemical bonding between atoms, and can be interpreted
by first-principles calculations in favorable cases.
However, a quantitative interpretation of ELNES maps
at atomic resolution requires to also take into account the
channeling characteristics of the swift electron beam
before and after the inelastic event [15,22–25],and
resulting EELS signal mixing. The appropriate description
and/or deconvolution of the electron beam propagation
allows for the precise determination of the origin of
spatially resolved variations in fine structures arising from
orbital orientation [26] and localization [27]. It has been
theoretically predicted that aberration-corrected STEM-
EELS should allow for the mapping of electronic orbitals
[24]. A first experimental proof of principle was reported
through real-space mapping of electronic transitions to Ti
dorbitals in bulk rutile TiO2[27], but thus far, mapping
electronic orbitals in real space remains extremely chal-
lenging and elusive, be it in bulk crystals or at crystal
imperfections and discontinuities.
Graphene, a flagship two-dimensional material with
exceptional physical and mechanical properties, has
received tremendous scientific interest for potential
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
and DOI.
PHYSICAL REVIEW LETTERS 128, 116401 (2022)
0031-9007=22=128(11)=116401(6) 116401-1 Published by the American Physical Society
electronic applications [28,29]. The atomic scale analysis
of individual graphene flakes is almost exclusively
achieved in the top surface view, thus enabling a path to
probe single atom chemical bonding [30–32] and phononic
response [33]. The chemical bonding in graphene can be
described as in-C-plane (σ) and orthogonal out-of-C-plane
(π) covalent bonds. The ELNES of the C-K edge therefore
represents the excitation of core states probing in-C-plane
σ(1s→2px;y) orbitals and out-of-C-plane π(1s→2pz)
orbitals, as illustrated schematically in Fig. S1 [49]. While
πstate distributions around nitrogen and boron dopants
in monolayer graphene have been evidenced from the
ELNES [34], the prospect of mapping orbitals at vacancies
and nitrogen dopants in a single graphene sheet has
been explored theoretically only a few years ago [35].
Nevertheless, even if this is intuitively the appropriate
direction to observe individual in-C-plane σbonds, inelas-
tic channeling computations show that the STEM-EELS
mapping of σorbitals in top surface view in pristine
graphene is not possible due to symmetry constraints
[35,36]. The observation of graphene layers in side view,
however, provides a pathway to directly visualizing the
distribution of πstates at the atomic scale using STEM-
EELS. While the description of the atomic scale distribu-
tion of out-of-C-plane πand in-C-plane σstates may
appear simple enough from a chemical bonding perspec-
tive, experimental evidence using STEM-EELS is lacking.
Moreover, considering the aforementioned subtle effects
associated with the localization of the EELS signal, due for
instance to channeling of the incident electron beam, the
interpretation of energy-filtered real-space maps can be
very complex and must be validated through careful
numerical work.
In this Letter, real-space maps of πand σstates in
epitaxial graphene multilayers are recorded in side view,
combining state-of-the-art high spatial and energy resolu-
tion STEM-EELS with inelastic channeling calculations.
The interpretation of the spatial distribution of orbital
signals, based on the excellent agreement between com-
puted and experimental data, highlights the successful
direct mapping of the πstate distribution at atomic reso-
lution in the transmission electron microscope. The theo-
retical approach provides a powerful platform to determine
the origin of the energy-filtered signal.
The epitaxial graphene/SiC specimen was synthesized
by thermal decomposition of SiC at 1300 °C in ultrahigh
vacuum (UHV). For completeness, and as shown in
Fig. 1(a), we note that a thin capping film of Bi2Se3
was additionally deposited on top of the graphene layers by
molecular beam epitaxy at 275–325 °C [37]. This specimen
was selected due to the convenient cross-section geometry
of the graphene layers; the properties and electronic
structure of interfaces with the 6H−SiC substrate and
the Bi2Se3capping film are the subject of separate studies
and not discussed here. This results in a structure
comprising of a so-called graphene “buffer layer”(BL)
in contact with the underlying SiC substrate, capped with a
number of layers of “epitaxial”graphene [here five such
layers are seen in Fig. 1(a)], whose macroscopic properties
are known to be nigh-on identical to those of free-standing
graphene [38,39].
The cross-section STEM lamellae were prepared by
focused ion beam milling. The thickness of the specimen
in the regions of investigation was evaluated to ∼25 nm by
Fourier-Log deconvolution of low-loss EELS spectra [11].
The STEM-EELS experiments were carried out using a
Nion HERMES microscope, equipped with a high-energy-
resolution monochromator, a Csaberration corrector up to
the fifth order, a Gatan Enfinium spectrometer, and oper-
ated at 60 kV. The convergence and collection semiangles
were 30 and 66 mrad, respectively. The specimen was
oriented in the ½10 ¯
10zone axis of SiC, corresponding to
the ½21 ¯
30zone axis of graphene (see Fig. S1 [49]). The
C-K edge was acquired with a 1.1 Å probe size and a step of
∼0.3Å, providing high spatial sampling while preserving
(a)
(b)
FIG. 1. (a) High resolution STEM-HAADF image of a six-layer
epitaxial graphene assembly, grown on 6H−SiC and topped
with Bi2Se3, simultaneously acquired with core-loss EELS data.
(b) C-K edge spectra corresponding to the probe positionned in-
C-plane (solid orange line) and between layers (solid blue line),
as indicated in (a). Spectra are integrated over the width of the
whole image, presented after background subtraction, and shifted
vertically for visualization.
PHYSICAL REVIEW LETTERS 128, 116401 (2022)
116401-2
the specimen from electron beam damage. The monochro-
mator slit width was adjusted to provide an effective energy
resolution of ∼100 meV, as measured at the zero-loss
peak full width at half maximum. While not the highest
achievable resolution on the instrument, these conditions
provided a good compromise of beam current (given the
chosen probe size) while still being narrower than expected
spectral features. The presented STEM-EELS dataset was
acquired from a region of 4.8×3.9nm2, with a sampling
of 110 ×88 pixels2. Subpixel scanning (16 ×16)was
employed, hence leading to a 1760 ×1408 pixels2simul-
taneously acquired HAADF image in Fig. 1(a). The
experimental EELS maps and HAADF image in Fig. 2
are directly cropped from a 88 ×88 pixels2region in the
original dataset. The dwell time was 0.2 s, at a dispersion of
0.05 eV=pixel. The experimental maps were obtained after
background extraction (modeled with a power-law func-
tion), and energy filtering with a 2 eV window for πand σ
states.
The spatial variations of the C-K ELNES are highlighted
in Fig. 1(b), where spectra corresponding to in-C-plane
(solid orange line) and out-of-C-plane (solid blue line)
probe positions are displayed. It is noteworthy that the
instrumental broadening of the electron source is narrower
than the intrinsic linewidth of the fine structures. This is
expected to facilitate orbital mapping since the spectral
features are not limited by the energy resolution of the
electron source but by physical phenomena linked to, e.g.,
the excited state lifetime broadening, core-hole screening,
or other multielectronic interactions. The πand σfine
structures are in good agreement with existing work on
free-standing graphene layers [39,40], with a sharp exci-
tonic feature visible around 294.5 eV. Although the edges
overall look comparable for the in- and out-of-C plane
probe positions, the πintensity increases noticeably
between the epitaxial graphene layers at out-of-C-plane
positions. This behavior was systematically observed and is
characteristic of all C-K near-edge structures between the
epitaxial graphene layers Gr2–Gr6 (see Fig. S2 [49]). The
ELNES of the BL and between the graphene BL and Gr2
are influenced by significant covalent bonding between the
graphene BL and SiC [39], and thus are not considered
here. In a first approximation, the spectral variations
observed for the Gr2–Gr6 graphene layers can be related
to the simple picture of out-of-C-plane delocalization of π
states, in contrast to the in-C-plane nature of σstates.
Indeed, while the πbonding takes place between C
neighboring atoms of a single graphene layer, the lobes
of the antibonding πorbitals are delocalized around the C
planes, as shown schematically in Fig. S1 of the
Supplemental Material [49]. On the contrary, the σorbitals
are contained essentially within the graphene planes.
Nevertheless, the magnitude of this out-of-C-plane delo-
calization measured by fine structure mapping, and the
ability to spatially distinguish πfrom σstates using a
convergent electron-probe in STEM-EELS are nontrivial.
In order to rationalize experimental findings, we carried
out extensive numerical calculations of the fine structure
maps. The effect of the graphene-SiC interface, partially
influenced by covalent bonding, and of the graphene-
Bi2Se3interface on orbital mapping are beyond the scope
of this Letter, therefore a structure made exclusively of
graphene layers was considered for inelastic channeling
calculations. For simulating the elastic electron propagation
both before and after the inelastic scattering events, the
multislice algorithm [41,42] was used. For the inelastic
interaction between the probe beam and the sample
electrons, we calculate the mixed dynamic form factor
[24,43], based on density functional theory data obtained
with WIEN2k [44]. All simulated STEM-EELS maps were
(a) (b) (c) (d) (i)
(e) (f) (g) (h)
FIG. 2. (a),(b),(c),(d) Experimental π,σ,π=σmaps, and HAADF image, respectively. (e),(f),(g),(h) Theoretical π,σ,π=σmaps
with shot noise, and ADF image, respectively. The position of atomic planes from the HAADF signal is indicated with green circles.
(i) π=σprofiles from (c),(g), and HAADF intensity integrated in the range indicated by the vertical orange, blue, and red bars in (c),(g),
and (d). All scale bars indicate 1 nm.
PHYSICAL REVIEW LETTERS 128, 116401 (2022)
116401-3
calculated with the same parameters (acceleration voltage,
convergence or collection angle, orientation, sampling,
etc.) as used in the experiments. For Fig. 2, the simulated
ideal maps were blurred using a Gaussian filter with a
standard deviation of 1.1 Å to mimic instrumental broad-
ening due to partial coherence of the electron source [45].
Subsequently, shot noise was added based on the exper-
imental noise characteristics, which were evaluated from
the electron intensity in the experimental maps; π:
31676.4, σ:40026.5e−=nm2.
The experimental πand σmaps, shown in Figs. 2(a)
and 2(b), respectively, both display higher intensity where
the Cplanes are located. The localization of the σstates on
the Cplanes is expected. For the πstates (which one might
expect to be stronger around the Cplanes), the apparent,
counterintuitive localization on the planes can be explained
by channeling effects of the electron beam. These obser-
vations are confirmed in the computed maps obtained by
inelastic channeling simulations in Figs. 2(e) and 2(f).
Rather than analyzing the absolute intensities, we inves-
tigate the ratio between the πand the σintensities as
shown in Figs. 2(c) and 2(g), as a way to normalize the π
intensity variations. The ratio is maximized between the C
planes in these maps, as exemplified by the vertical π=σ
profiles plotted versus the HAADF intensity in Fig. 2(i).
HAADF intensity minima coincide with π=σintensity
profile maxima, which are almost exactly equidistant
from two graphene layers. The visual agreement between
the calculated and experimental π,σ, and π=σmaps is
supported by the remarkable overlap of the calculated
and experimental π=σline profiles. This successful
reproduction of the experimental data underlines the
robustness of the inelastic channeling calculations per-
formed in this work to interpret the experimental spectral
data. Most importantly, this result provides an undeniable
proof that the contrast obtained from πand σreal-space
fine-structure maps at high resolution does match the
expected localization of corresponding unoccupied elec-
tronic orbitals. It also highlights that beyond the atomic site
where core-level excitation takes place, the localization of
the πand σorbitals in two-dimensional maps is inti-
mately linked to the channeling of the electron beam, and is
thus strongly affected by the specimen projected thick-
ness [46].
While the channeling of the swift electron beam pri-
marily depends on the alignment of the electron beam path
with the atomic columns, the projected thickness also
strongly modifies the atomic-scale contrast in fine structure
maps. To evaluate the influence of the projected thickness
on the expected πand σorbital contrast, we performed
inelastic channeling calculations using the same simulation
parameters as in Fig. 2but considering specimens with
different thicknesses: 0.43 (a single graphene unit cell),
12.8, and 25.6 nm. The latter corresponds to the estimated
thickness of the TEM lamella considered experimentally.
The πand σmaps corresponding to these projected
thicknesses under ideal conditions (no noise, no instru-
mental broadening, etc.) are presented in Figs. 3(c) and
3(d), respectively. These maps differ from those displayed
in Figs. 2(e),2(f), which contain noise and instrumental
broadening. The πmap of the thinnest specimen displays
lobes outside the Cplanes, in agreement with the πcharge
(a) (c)
(b) (d)
FIG. 3. (a) Charge density for the energy interval between 0.73 and 3.46 eVabove the Fermi level. (b) Projected density of states in
graphite. The zaxis corresponds to the crystallographic caxis of graphite, perpendicular to the carbon layers. (c) πmaps for projected
thicknesses of 0.43 (left), 12.8 (middle), and 25.6 nm (right). The position of atomic planes is indicated with green circles. (d) σmaps
for the same thicknesses. All maps are shown without noise and instrumental broadening. All scale bars indicate 5 Å.
PHYSICAL REVIEW LETTERS 128, 116401 (2022)
116401-4
density in Fig. 3(a). Additional intensity is also visible on
the Ccolumns, and becomes more prominent for larger and
more realistic projected thicknesses. At a thickness of
25.6 nm, the intensity of the πstates on the Ccolumns
is stronger than outside the Cplanes, in agreement with the
experimental πmaps in Fig. 2. For all thicknesses, it is
noteworthy that the intensity in the πmaps is expected to
fade out beyond ∼1Å away from the Cplanes. The
intensity in the σmaps is, as expected, exclusively
contained within the Cplanes, and peaked on the C
columns. In addition, it is noteworthy that the atomic
resolution contrast is smoothed out with increasing thick-
ness. It should be noted that the σmaps also contain some
intensity from pzstates, i.e., states with πsymmetry, as
shown in the PDOS in Fig. 3(b).
These simulated fine structure maps, in which the elastic
channeling conditions of the electron beam were taken into
account, highlight the fact that the specimen thickness must
be considered carefully to interpret STEM-EELS orbital
mapping experiments successfully. Halving the projected
thickness down to 12.8 nm is expected to lead to a result
similar to the current experimental thickness of 25.6 nm.
The direct comparison of πorbital maps with the πcharge
density plot in Fig. 3(a) is not reasonable for the exper-
imental thickness considered, nor even for 12.8 nm, but
only for an unrealistically small thickness of the order of
0.43 nm. Therefore, it is suggested that smaller projected
thickness will only be meaningful below few nm to provide
better visualization of electronic orbitals using STEM-
EELS in the present case. The noise level is also a major
hurdle to overcome, and is clearly visible when comparing
the πand σmaps in Figs. 2(e) (shot noise added) and 3(c)
(no shot noise), and Figs. 2(f) (shot noise added) and 3(d)
(no shot noise), respectively. It is expected that orbital
mapping in STEM-EELS might benefit from a new gen-
eration of detectors with improved sensitivity and lower
noise level [47,48].
In conclusion, the spatial distribution of antibonding π
and σorbitals in epitaxial graphene multilayers was
mapped successfully by electron energy-loss spectroscopy
in the aberration-corrected scanning transmission electron
microscope. Inelastic channeling calculations unambigu-
ously reproduce the experimental πand σorbital maps
with high level of accuracy, and demonstrate the decisive
effect of the specimen thickness on the orbital mapping
capabilities in graphene. The real-space visualization, at
atomic resolution, of unoccupied electronic states with
different symmetry defines a pathway to better understand
chemical bonding at interfaces and defects in solids. This is
particularly relevant to foster defect engineering and tune
the properties of solids for a wide range of promising
applications where physical and chemical phenomena
occur at surfaces (e.g., photocatalysis) or interfaces (e.g.,
spintronics). This work further illustrates the potentiality of
orbital mapping using STEM-EELS.
The electron microscopy work was supported by the
EPSRC (UK). SuperSTEM Laboratory is the EPSRC
National Research Facility for Advanced Electron
Microscopy. The authors would like to thank Hitachi
High-Tech Corporation (UK and Japan), Orsay Physics
and Tescan for the preparation of FIB lamellae. M.B. is
grateful to the SuperSTEM Laboratory for microscope
access, and to the School of Chemical and Process
Engineering at the University of Leeds for a visiting
associate professorship and financial support. M. E. and
S. L. acknowledge funding from the Austrian Science Fund
(FWF) under Grant No. I4309-N36. L. L. acknowledges
funding from U.S. National Science Foundation under
Grant No. EFMA-1741673.
M. B. and M. E. contributed equally to this work.
*mbugnet@superstem.org
†stefan.loeffler@tuwien.ac.at
‡dmkepap@superstem.org
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PHYSICAL REVIEW LETTERS 128, 116401 (2022)
116401-6
