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APPLIED PHYSICS
Coherent charge hopping suppresses photoexcited
small polarons in ErFeO
3
by antiadiabatic
formation mechanism
Ye-
Jin Kim
1
, Jocelyn L. Mendes
1
, Jonathan M. Michelsen
1
, Hyun Jun Shin
2
, Nara Lee
2
,
Young Jai Choi
2
, Scott K. Cushing
1
*
Polarons are prevalent in condensed matter systems with strong electron-
phonon coupling. The adiabaticity of
the polaron relates to its transport properties and spatial extent. To date, only adiabatic small polaron formation
has been measured following photoexcitation. The lattice reorganization energy is large enough that the first
electron–optical phonon scattering event creates a small polaron without requiring substantial carrier thermal-
ization. We measure that frustrating the iron-
centered octahedra in the rare-
earth orthoferrite ErFeO
3
leads to
antiadiabatic polaron formation. Coherent charge hopping between neighboring Fe
3
+
Fe
2
+
sites is measured
with transient extreme ultraviolet spectroscopy and lasts several picoseconds before the polaron forms. The re
-
sulting small polaron formation time is an order of magnitude longer than previous measurements and indicates
a shallow potential well, even in the excited state. The results emphasize the importance of considering dynamic
electron-
electron correlations, not just electron-
phonon–induced lattice changes, for small polarons for trans-
port, catalysis, and photoexcited applications.
INTRODUCTION
The interaction between charge carriers and a polar lattice can lead to
charge localization by the local lattice deformation which is referred to
as polaron formation. Polarons are of major interest for semiconduct-
ing, superconducting, and insulating materials because they dominate
transport properties (
1
4
). In the strong-
coupling limit, sublattice-
sized
small (Holstein) polarons (
5
,
6
) reconfigure electronic states to control
surface reactivity (
7
,
8
), ion mobility (
9
,
10
), and high-
temperature su-
perconductivity (
11
). Understanding how the relationship between
strong electron-
phonon coupling and electron correlations controls po-
laron formation is important from both a ground-
state materials and
photodynamics perspective.
Optical excitation can generate electron and hole polarons by
photodoping the lattice (
12
17
). To date, photoexcited small polar
-
ons are measured to form within the first electron–optical phonon
scattering event, even when the charge carrier has excess energy
above the band edge (
16
,
18
23
). Within the Hubbard-
Holstein
model for correlated electron materials, this indicates that the reor
-
ganization energy (electron-
phonon coupling strength) of the small
polaron is larger than the hopping integral between metal sites (
24
).
The hundreds of femtoseconds small polaron formation is termed
adiabatic as it occurs without substantial thermalization. In this
case, the photoexcited small polaron formation is almost an impul-
sive excitation.
In this study, we measure that the distorted FeO
6
octahedron in
erbium iron oxide (ErFeO
3
), a rare-
earth orthoferrite, leads to antia-
diabatic small polaron formation using transient extreme ultraviolet
(XUV) spectroscopy. Photoexcitation of a ligand-
to-
metal charge-
transfer transition creates an axially elongated FeO
6
octahedron.
Multiple coherent charge hopping events are then measured be-
tween neighboring Fe
3
+
Fe
2
+
sites. The coherent charge hopping is
associated with an optical phonon mode that modulates the dis-
tance between the neighboring Fe
O
Fe bonds. The charge hop-
ping continues until the photoexcited carriers thermalize and small
polaron formation occurs on a picosecond timescale, as is charac-
teristic of an antiadiabatic interaction (
25
). The polaron formation
time is an order of magnitude longer than previously measured (
16
,
18
,
20
23
). The lattice reorganization energy estimated from the ex-
periments is also smaller than the magnitude of the hopping inte-
gral, roughly estimated by the Fe
d
-
orbital conduction band width,
in line with time-
dependent Holstein and Hubbard-
Holstein model
predictions for the conditions of excited-
state antiadiabatic polaron
formation.
Overall, our measurements confirm that dynamical electron cor
-
relations play a critical role in controlling small polaron formation
in correlated electron materials and must be considered beyond just
the lattice reorganization energy (
26
). This result is in contrast to a
variety of previous studies in other Fe
O materials where changes
to defects, dopants, spin, and symmetry always lead to a similar,
adiabatic small polaron formation time, suggesting that knowledge
of the reorganization energy alone was sufficient to compare the dy-
namics (
16
,
18
23
). The measured interplay between optical pho-
nons, electron correlations, and local lattice deformation provides a
clear picture of how antiadiabatic excited-
state polaron formation
occurs. The measurement of the conditions under which antiadia-
batic polaron formation occurs is also important to a broad range of
small polaron-
dominated applications such as polaronic supercon-
ductivity theories, charge-
density wave ordering, antiferromagnet-
ism, and charge transport in both solid-
state and molecular systems
(
27
29
). For example, using high-
frequency phonons and their in-
stantaneous response to photoexcitation in the antiadiabatic regime
is proposed for tuning electron correlations to modulate metallicity in
relation to Peierls ordering (
30
,
31
). Moreover, by confirming gen-
eral Hubbard-
Holstein model predictions with the experimental
evidence of the excited-
state behavior, the measurements increase
our fundamental understanding of how strong electron-
phonon
1
division of chemistry and chemical engineering, c
alifornia i
nstitute of
technolo
-
gy, Pasadena, c
A 91125, USA.
2
department of Physics, Yonsei University, Seoul
03722, Republic of Korea.
*c
orresponding author. email: scushing@
caltech.
edu
copyright © 2024
the
Authors, some rights
reserved; exclusive
licensee American
Association for the
Advancement of
Science. no claim to
original U.S.
Government Works.
distributed under a
creative c
ommons
Attribution
nonc
ommercial
license 4.0 (
cc BY- nc
).
Kim
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coupling unfolds in correlated electron systems in nonequilibrium
situations.
RESULTS AND DISCUSSION
ErFeO
3
is an antiferromagnetic, charge-
transfer insulator that crys-
tallizes in an orthorhombically distorted perovskite structure with
the space group
Pbnm
, as confirmed by x-
ray diffraction (note S1,
fig. S1, and table S1) (
32
) and depicted in Fig. 1A. It belongs to the
rare-
earth orthoferrite family RFeO
3
(where R is a trivalent rare-
earth cation) and features corner-
shared FeO
6
octahedra that are
orthorhombically distorted and orthorhombically rotated about the
[001] axis (
33
). ErFeO
3
exhibits rich magnetic properties arising
from the magnetic transitions between the 3
d
and 4
f
electrons of
Fe
3
+
and Er
3
+
ions, respectively. These properties include a high
Néel temperature (
34
), large magnetoelectric coupling (
35
), and ul-
trafast optical control of spins (
36
,
37
), making it a potential room-
temperature multiferroic candidate. Here, we use this control of the
frustrated lattice versus electron correlations to explore the struc-
tural factors that determine small polaron formation.
Figure 1 (B and C) presents the calculated electronic structure of
ErFeO
3
by using density functional theory (DFT) with the Hubbard
U correction (DFT
+
U). The calculations give a charge-
transfer
bandgap of approximately 1.8 eV (calculation details in note S2.1
and fig. S2), which is consistent with the measured charge-
transfer
optical absorption feature at 1.8
±
0.1 eV (fig. S3). Within the ap-
proximations of DFT
+
U (
38
), the calculated projected density of
states (PDOS) in Fig. 1B has a valence band that predominantly con-
sists of O 2
p
orbitals and a conduction band predominantly of lower-
lying Fe 3
d
and higher-
lying Er 5
d
orbitals (
39
,
40
). The optical
excitation used in these experiments, at 3.1 eV (400 nm), promotes
electrons from the O 2
p
orbital to the unoccupied Fe 3
d
orbital
through a ligand-
to-
metal charge-
transfer transition. The calculated
band structure in Fig. 1C along high-
symmetry
k
- points reveals that
the valence band maximum and the conduction band minimum are
flat from the
Γ
- to Y-
points of the Brillouin zone, indicative of strong
electron correlations (
41
), similar to other rare-
earth orthoferrites
(
42
,
43
).
Transient XUV spectroscopy is used to measure element-
specific
electron and hole dynamics following a ligand-
to-
metal charge-
transfer photoexcitation. Time-
resolved differential absorption spec-
tra are collected at the Fe M
2,3
edge around 54 eV, which corresponds
to a transition from the 3
p
3/2,5/2
core states to the 3
d
valence state. The
sample is photoexcited with a 50-
fs pulse at a pump fluence of 3 mJ/
cm
2
under ambient temperature (293 K). The differential absorption
signal,
Δ
A
, is calculated as
Δ
A
=
log(
R
off
/
R
on
), where
R
off
and
R
on
are
the XUV reflectance spectra with the pump beam blocked and un-
blocked, respectively. High harmonic generation creates the XUV
probe pulse (upper panel in Fig. 2A) from a few-
cycle white light
pulse in an argon gas medium (experimental details in note S3 and
fig. S4) (
44
). By using a grazing incidence angle of 10°, the XUV
probe has a penetration depth of approximately 2 nm, providing a
surface-
sensitive geometry (
44
,
45
). In the previous measurement of
small polaron formation times in
α
- Fe
2
O
3
, bulk versus surface mea-
surements only showed variations in the 30% range (
18
), smaller
than the order of magnitude change in small polaron formation time
measured here.
The time-
resolved differential absorption spectra are shown in
Fig. 2A as a pseudo-
color plot (see fig. S5 for the temporal lineout
spectra). The first 5 ps after photoexcitation are plotted, after which
the dynamics reach a steady state out to the 1-
ns measurement limit
of our instrument (fig. S6). The core-
level transition Hamiltonian
for the Fe M
2,3
edge is dominated by angular momentum compo-
nents (
46
). The increase and decrease in absorption in the XUV
spectrum therefore do not directly relate to electron and hole ener
-
gies but instead relate to the change in overall Fe site occupation
(oxidation state), the presence of phonon modes, and other struc-
tural excitations such as small polarons (
46
,
47
).
Fig. 1.
Electronic and lattice structure of ErFeO
3
.
(
A
) c
rystal structure of erFeO
3
. the crystal has a distorted perovskite structure with an orthorhombic symmetry.
corner- sharing FeO
6
octahedra are distorted because of the presence of an er
3
+
ion. erFeO
3
is photoexcited with 50-
fs, 3.1-
ev pump pulses while XUv pulses probe pho
-
toinduced dynamics of the material.
the unit cell of the crystal is indicated with a dotted box. (
B
)
calculated total PdOS of
erFeO
3
. Photoexcitation generates holes (a white
circle) and electrons (a black filled circle) in the O 2
p
and Fe 3
d
bands, respectively.
E
F
is the Fermi energy. (
C
)
calculated band structure of
erFeO
3
along the high-
symmetry
k
- points.
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The spectral evolution exhibits two distinctive vectors and times-
cales within the 5-
ps time frame, which can be confirmed by singular
value decomposition (
20
,
48
) (see overlays in Fig. 2A). An excited-
state
approximation to the Bethe–Salpeter equation (BSE) is used to inter
-
pret the spectral contributions (
49
,
50
). Briefly, the OCEAN (Obtain-
ing Core Excitations from the Ab initio electronic structure and the
NIST BSE solver) code is modified using an adiabatic approximation
of the photoexcited electronic states or lattice distortions to calculate
the change in the core-
valence excitons that make up the XUV spectra
(calculation details in note S2.2) (
44
,
46
,
47
). The initial photoexcited
charge-
transfer state creates four distinct bands positioned at 51.6,
52.1, 54.1, and 54.5 eV when compared to the Fe
3
+
ground state, which
can be assigned to
e
g
,
b
2g
,
a
1g
, and
b
1g
multiplets, respectively (
51
)
(Fig. 2B). A local elongation of the Fe
O bond in the axial direction,
and a contraction of the equatorial in-
plane bonds from the Jahn-
Teller distortion (fig. S7), must also be included. The interatomic dis-
tance between neighboring Fe sites decreases because of this distortion
(
52
). Next, at a pump-
probe time delay of
t
=
1 ps, the main spectral
feature at 54-
eV blue shifts. This spectral shift of 100
±
10 meV (fig. S5),
which also results in changes to the
e
g
and
b
2g
spectral amplitudes over
time, corresponds to the formation of the small polaron (
16
,
20
,
23
).
This is modeled as an overall expansion of the Fe
O bonds, and good
agreement exists between theory and experiment in both cases.
The kinetics of the small polaron formation are determined using
the assigned spectral features. A multivariate regression analysis using
the spectral components is depicted in Fig. 3A. A three-
state sequen-
tial kinetic model is used for the best fit as outlined in Fig. 3B (fitting
details in note S4 and fig. S8), including the 50-
fs photoexcitation
pulse. The kinetic model is consistent with past small polaron forma-
tion studies (
20
,
21
) so that relative timescales can be compared. The
initial charge-
transfer state thermalizes on the order of
τ
1
=
250
±
80 fs,
but small polaron formation is delayed by
τ
2
=
2.3
±
0.3 ps with the
incorporation of an intermediate step. This is characteristic of a bal-
ance between carrier thermalization and small polaron formation
through the coherent charge hopping in the antiadiabatic regime as
discussed in the next paragraph.
Further insight into the small polaron formation process is given
by the coherent oscillations in the transient XUV spectra. Figure 3C
shows coherent oscillations for lineouts at 53.2 and 52.2 eV. The main
decrease in absorption observed at 52.8 to 54.7 eV is indicative of the
depletion of the initial Fe
3
+
state, while the main increase in absorp-
tion in the red-
shifted region of 51.5 to 52.8 eV signifies the forma-
tion of the Fe
2
+
state following photoexcitation, based on the spectral
assignment (see figs. S7, S9, and S10 for the full spectrum and analy-
sis). The coherent oscillations have a periodicity of approximately
170 fs, corresponding to a frequency of around 5.0 THz (170 cm
1
).
The measured oscillation frequency can be correlated with a Raman-
active optical phonon mode with
A
g
symmetry that corresponds to a
rocking motion of the FeO
6
octahedra between the Er
3
+
ions (
33
,
53
); see the schematic in Fig. 3D. The optical phonon mode leads to
coherent charge hopping between neighboring Fe sites by modulat-
ing the Fe
O
Fe bond length, as evidenced by the 180° out-
of-
phase
oscillating signal between the Fe
3
+
and Fe
2
+
signals (Fig. 3D). The
coherent charge hopping events in Fig. 3C do not onset until carrier
thermalization has occurred, matching the timescale of
τ
1
from
Fig. 3A. Similarly, small polaron formation is not complete in Fig. 3A
Fig. 2.
Photoinduced structural distortion and small polaron formation.
(
A
)
high-
order harmonic profile for the XUv probe pulses (top).
the color scale corresponds
to the normalized harmonic intensity.
two-
dimensional false color plot of time-
resolved differential absorption spectra obtained at a pump fluence of 3 mJ/cm
2
(bottom).
the color scale corresponds to differential absorbance (
Δ
A
). Spectral vectors for singular value decomposition are overlaid, representing the charge-
transfer (top) and the
polaron states (bottom).
the spectral blue shift of the main absorption feature at
~
54 ev
, typically indicative of small polaron formation, is measured as 100
±
10 mev
. d
otted
lines represent the fitted spectral shift (fig. S5). (
B
) c
alculated differential absorption spectra compared to the primary spectral vectors. For the charge-
transfer state, the
FeO
6
octahedron is axially elongated because of an optical phonon within our temporal resolution, giving rise to crystal field splitting, as shown in the calculated excited-
state absorption spectra of Fe
2
+
(dotted line). State-
filling effects were incorporated for the photoexcited electrons and holes. For the polaron state, six Fe
O bonds in the
octahedron are expanded with the overall enlargement of the unit cell.
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until after the multiple coherent charge hopping events decay in
Fig. 3C, matching
τ
2
, designating the process as antiadiabatic.
Transient XUV measurements, therefore, provide a detailed pic-
ture of antiadiabatic small polaron formation (Fig. 4). The photoex-
cited electrons of the axially elongated FeO
6
octahedra thermalize
through scattering with optical phonon modes, some of which cor
-
respond to FeO
6
octahedral rotations within the Er
3
+
sublattice. The
octahedral rotations modulate Fe
O
Fe bond lengths, leading to a
periodic hopping between sites. Only after multiple electron–
optical
phonon scattering events does the electron hopping decay, corre-
sponding to the creation of the small polaron. The small polaron does
not lead to recombination within the hundreds-
of-
picoseconds tim-
escale of the transient XUV measurement. The measured small po-
laron formation process is in contrast with the previously measured
adiabatic mechanism, wherein the small polaron forms immediately
within the first electron–optical phonon scattering event without
substantial carrier thermalization (
16
,
18
,
20
23
).
The Hubbard-
Holstein model predicts that the adiabaticity of
small polaron formation depends on the balance of the hopping
integral between Fe sites and the small polaron reorganization
energy. The Hamiltonian for the Hubbard-
Holstein model (
5
,
54
)
is shown as
where
c
i
σ
and
c
i
σ
are the creation and annihilation operators for an elec-
tron with spin
σ
at site
i
, respectively.
b
i
and
b
i
are the phonon creation
and annihilation operators, respectively.
n
i
σ
is the on-
site electron-
phonon coupling density of
c
i
σ
c
i
σ
with strength
g
, which reflects the
electron-
phonon coupling and therefore polaron reorganization en-
ergy. The Coulomb repulsion between electrons are characterized by
the on-
site interaction strength,
U
. The hopping amplitude is denoted
by
t
h
, and
ω
0
is a dispersionless phonon frequency. The reorganization
energy is typically parameterized by the phonon frequency and defor
-
mation potential, balanced with the on-
site interaction.
Previous studies on
α
- Fe
2
O
3
demonstrated that the blue shift of
the main XUV spectral feature can be related to the small polaron
H
=−
t
h

<
ij
>
,
σ
(
c
i
σ
c
j
σ
+
H
.
c
.)
+
U

i
n
i
n
i
0

i
b
i
b
i
+
g

i
,
σ
n
i
σ
(
b
i
+
b
i
)
(1)
Fig. 3.
Kinetic model of the relaxation dynamics and coherent hopping motions.
(
A
)
the time-
dependent amplitude of the charge-
transfer and polaron states using
a multivariate regression of the experimental data. A three-
state model was used to incorporate the intermediate step of the charge hopping events in the antiadiabatic
regime.
the amplitudes are fitted with a rate equation model for small polaron formation (solid and dotted lines). (
B
) Schematic of the three-
state sequential kinetic
model with the three time constants of
τ
1
,
τ
2
, and
τ
3
. (
C
)
the coherent modulation of transient signals extracted at 53.2 and 52.2 ev
, representing the main absorption of
Fe
3
+
and Fe
2
+
, respectively. Oscillations from the initial electron–optical phonon scattering lead to coherent hopping between the photoexcited Fe
3
+
and its Fe
2
+
nearest
neighbors.
the fast Fourier transforms (FFt
) are shown on the right. (
D
) the out-
of-
phase oscillations between the Fe
3
+
and Fe
2
+
spectral features at
Δ
t
between 0.3 to 0.6 ps
indicative of the charge-
hopping process that delays small polaron formation in the antiadiabatic regime.
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reorganization energy (
16
,
18
23
). In these studies, a spectral shift of
~
1 eV corresponded to a formation energy of 0.4 to 0.6 eV, consistent
with the theoretical predictions. Here, the measured spectral shift is
100
±
10 meV, which is
1
/
10
of the reported value for
α
- Fe
2
O
3
. This
would bound the small polaron formation energy of ErFeO
3
as
<
100 meV,
or
<
50 meV if the same XUV relation holds. In support of this estimate,
the polaron formation rate is roughly
1
/
10
of that reported for
α
- Fe
2
O
3.
t
h
can be bounded as
<
300 meV by the half-
bandwidth of the relevant
Fe 3
d
conduction band (
~
0.6 eV; Fig. 1B), and
ω
0
corresponds to the
measured phonon energy at approximately 20 meV (Fig. 3C).
A time-
dependent solution of the Hubbard-
Holstein model is need-
ed to parameterize the antiadiabatic excited-
state small polaron forma-
tion (
25
). In ground-
state solutions to the Hubbard-
Holstein or Holstein
model, the “adiabaticity ratio” parameterization of
ω
0
/
t
h
would here
denote an adiabatic regime for polaron hopping (
26
,
55
,
56
). In the
ground state, adiabatic refers to whether the lattice changes instanta-
neously upon polaron motion and should not be confused with the
excited-
state or nonequilibrium definition of adiabaticity used in this
paper, which refers to the formation time after photoexcitation
.
The
measured coherent electron hopping and decreased polaron formation
energy is consistent, however, with ground-
state definitions of a “large”
polaron regime but transport measurements are needed before further
comment can be made.
Our measurements therefore indicate that a complete picture of
photoexcited polaron formation in correlated electron systems must
include the balance of the charge hopping integral versus the lattice-
based reorganization energy. Usually, a Holstein-
like model is con-
sidered sufficient, focusing mainly on the reorganization energy, but
our results suggest that a full Hubbard-
Holstein-
like model needs to
be used when the polaron formation energy approaches the electron
bandwidth. The coherent charge hopping between Fe–Fe sites sug-
gests small polaron transport in ErFeO
3
requires a coordination of
phonons, electron correlations, and lattice deformations at adjacent
sites. This behavior is opposite to previous measurements of adiabatic
excited-
state dynamics where polaron hopping occurs only through a
phonon-
mediated lattice deformation (
16
,
18
,
20
23
).
MATERIALS AND METHODS
Experimental setup
The measurements were conducted using photoexcitation from
a
~
50-
fs, 400-
nm frequency-
doubled output of a BBO crystal with
Fig. 4.
Summary of the antiadiabatic photoinduced polaron formation dynamics in ErFeO
3
.
(
A
) Potential energy curves comparing small polaron formation in the
antiadiabatic (left) and adiabatic regimes (right). Upon photoexcitation, electrons instantaneously transfer from the O
2
to Fe
3
+
ions, generating photoexcited electrons
and holes in the conduction and valence bands, respectively. i
n the charge-
transfer state, the axial Fe
O bond is elongated, resulting in the splitting of the Fe 3
d
band at
a slightly shifted nuclear coordinate from the ground-
to excited-
state configurations (
Q
gr
Q
ex
). hot carriers in the high-
energy conduction band then thermalize in
hundreds of femtoseconds. i
n the antiadiabatic polaron formation of this work, coherent charge hopping between the Fe
3
+
and Fe
2
+
lasts for a few picoseconds, delaying
small polaron formation at
Q
polaron
, while electron tunneling is dominant in the adiabatic pictures. (
B
) Schematics of lattice deformation in erFeO
3
at the charge-
transfer
(
Δ
t
=
0) and polaron states (
Δ
t
>
0), where the FeO
6
octahedron axially elongates upon photoexcitation and then expands equally in all axes during the small polaron
formation.
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p
- polarization, pumped with an 800-
nm, 1-
kHz regeneratively ampli-
fied Ti:Sapphire laser (Legend Elite Duo, Coherent). The optical excita-
tion fluence was set to 3 mJ/cm
2
. Transient reflectance and differential
absorption signal were measured by varying delay times between the
excitation and probe pulses using an optomechanical delay stage. The
photoexcited electronic dynamics were probed with XUV pulses pro-
duced by high-
harmonic generation in argon gas medium with an
s
-
polarized few-
cycle white light pulse (
<
6 fs, 550 to 950 nm). The
residual white light beam was removed with a 200-
nm-
thick alumi-
num filter (Lebow). The generated XUV continuum was used to probe
the Fe M
2,3
absorption edge around 54 eV. An edge-
pixel referencing
scheme was used to denoise intensity fluctuations referenced to signal-
free spectral regions (
57
). The reflection measurement used a 10° graz-
ing incidence geometry (80° from normal incidence). The ground-
state
static XUV reflectivity of ErFeO
3
was obtained by normalizing the
measured static reflectance spectrum of ErFeO
3
to a silicon wafer,
which does not have any absorption features in the energy region of
interest. Neon gas was used for spectral calibration. The detailed in-
strumentation of the setup is described in note S3 and fig. S4.
Materials
Single crystals of ErFeO
3
were synthesized according to the details
outlined in note S1.
DFT and ab initio calculations
Calculation details are discussed in note S2.
Supplementary Materials
This PDF file includes:
notes S1 to S4
Figs. S1 to S10
table S1
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Acknowledgments:
We thank W.-
W Park at Ulsan national i
nstitute of Science and
technology
for measuring the diffuse reflectance spectrum. We also thank W. l
ee at c
alifornia i
nstitute of
technology for providing fruitful comments on the ab initio calculation. Any opinions,
findings, and conclusions or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the national Science Foundation.
the
computations presented here were conducted in the Resnick h
igh Performance c
omputing
center, a facility supported by the Resnick Sustainability i
nstitute at the c
alifornia i
nstitute of
technology.
this research used resources of the national energy Research Scientific
computing c
enter, a dOe Office of Science User Facility supported by the Office of Science of
the U.S. d
epartment of energy under c
ontract no. de-
Ac02-
05ch11231 using neRSc award
BeS- eR
cAP0024109.
the work at Yonsei University was supported by the national Research
Foundation of Korea (nRF) through grants, nRF-
2017R1A5A1014862 (SR
c program: vdWMR
c
center), nRF-
2021R1A2c1006375, and nRF-
2022R1A2c1006740.
the Uv
- vis diffuse reflectance
spectrum was acquired at the UniSt c
entral Research Facilities c
enter of Ulsan national
institute of Science and
technology.
Funding:
Y.-
J.K. is supported by the liquid Sunlight
Alliance (the U.S. d
epartment of energy, Office of Science, Office of Basic energy Sciences,
Fuels from Sunlight hub under award number de-
Sc0021266). J.l.M. acknowledges support
by the national Science Foundation Graduate Research Fellowship Program under grant no.
1745301.
Author contributions:
Y.-
J.K. performed the measurements with the initial technical
support of J.l.M. and J.M.M. Y.-
J.K. analyzed the data, carried out the ab initio calculations, and
prepared figures and the Supplementary Materials. h.J.S., n.l., and Y.J.c. fabricated and
characterized the specimen. S.K.c. supervised the project and provided guidance. Y.-
J.K. and
S.K.c. wrote the manuscript with the input from all authors.
Competing interests:
t
he authors
declare that they have no competing interests.
Data and materials availability:
All data
needed to evaluate the conclusions in the paper are present in the paper and/or the
Supplementary Materials.
Submitted 22 August 2023
Accepted 13 February 2024
Published 20 March 2024
10.1126/sciadv.adk4282