# Anisotropic structural dynamics of monolayer crystals revealed by
femtosecond surface x-ray scattering

I-Cheng Tung  Advanced Photon Source, Argonne National Laboratory, Argonne, IL
60439, USA  Aravind Krishnamoorthy  Collaboratory of Advanced Computing and
Simulations, University of Southern California, Los Angeles, CA 90089, USA
Sridhar Sadasivam  Center for Nanoscale Materials, Argonne National
Laboratory, Argonne, IL 60439, USA  Hua Zhou  Advanced Photon Source, Argonne
National Laboratory, Argonne, IL 60439, USA  Qi Zhang  Advanced Photon Source,
Argonne National Laboratory, Argonne, IL 60439, USA  Kyle L. Seyler
Department of Physics, University of Washington, Seattle, WA 98195, USA
Genevieve Clark  Department of Physics, University of Washington, Seattle, WA
98195, USA  Ehren M. Mannebach  Department of Materials Science and
Engineering, Stanford University, Stanford, CA 94305, USA  Clara Nyby
Department of Chemistry, Stanford University, Stanford, CA 94305, USA
Friederike Ernst  Department of Applied Physics, Stanford University,
Stanford, CA 94305  PULSE Institute, SLAC National Accelerator Laboratory,
Menlo Park, CA 94025, USA  Diling Zhu  SLAC National Accelerator Laboratory,
Menlo Park, CA 94025, USA  James M. Glownia  SLAC National Accelerator
Laboratory, Menlo Park, CA 94025, USA  Michael E. Kozina  SLAC National
Accelerator Laboratory, Menlo Park, CA 94025, USA  Sanghoon Song  SLAC
National Accelerator Laboratory, Menlo Park, CA 94025, USA  Silke Nelson  SLAC
National Accelerator Laboratory, Menlo Park, CA 94025, USA  Hiroyuki Kumazoe
Department of Physics, Kumamoto University, Kumamoto 860-8555, Japan  Fuyuki
Shimojo  Department of Physics, Kumamoto University, Kumamoto 860-8555, Japan
Rajiv K. Kalia  Collaboratory of Advanced Computing and Simulations,
University of Southern California, Los Angeles, CA 90089, USA  Priya Vashishta
Collaboratory of Advanced Computing and Simulations, University of Southern
California, Los Angeles, CA 90089, USA  Pierre Darancet  Center for Nanoscale
Materials, Argonne National Laboratory, Argonne, IL 60439, USA  Tony F. Heinz
Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA 94025,
USA  Stanford Institute for Materials and Energy Sciences, SLAC National
Accelerator Laboratory, Menlo Park, CA 94025, USA  Aiichiro Nakano
Collaboratory of Advanced Computing and Simulations, University of Southern
California, Los Angeles, CA 90089, USA  Xiaodong Xu  Department of Physics,
University of Washington, Seattle, WA 98195, USA  Aaron M. Lindenberg
Department of Materials Science and Engineering, Stanford University,
Stanford, CA 94305, USA  PULSE Institute, SLAC National Accelerator
Laboratory, Menlo Park, CA 94025, USA  Stanford Institute for Materials and
Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025,
USA  Haidan Wen<EMAIL_ADDRESS>Advanced Photon Source, Argonne National
Laboratory, Argonne, IL 60439, USA

###### Abstract

X-ray scattering is one of the primary tools to determine crystallographic
configuration with atomic accuracy. However, the measurement of ultrafast
structural dynamics in monolayer crystals remains a long-standing challenge
due to a significant reduction of diffraction volume and complexity of data
analysis, prohibiting the application of ultrafast x-ray scattering to study
nonequilibrium structural properties at the two-dimensional limit. Here, we
demonstrate femtosecond surface x-ray diffraction in combination with
crystallographic model-refinement calculations to quantify the ultrafast
structural dynamics of monolayer WSe2 crystals supported on a substrate. We
found the absorbed optical photon energy is preferably coupled to the in-plane
lattice vibrations within 2 picoseconds while the out-of-plane lattice
vibration amplitude remains unchanged during the first 10 picoseconds. The
model-assisted fitting suggests an asymmetric intralayer spacing change upon
excitation. The observed nonequilibrium anisotropic structural dynamics in
two-dimensional materials agrees with first-principles nonadiabatic modeling
in both real and momentum space, marking the distinct structural dynamics of
monolayer crystals from their bulk counterparts. The demonstrated methods
unlock the benefit of surface sensitive x-ray scattering to quantitatively
measure ultrafast structural dynamics in atomically thin materials and across
interfaces.

The development of van der Waals (vdW) materials has opened up possibilities
for the exploration of new physics in the two-dimensional (2D) limit
Novoselov:2016ik ; Ajayan:2016cd . Strong light-matter interaction in 2D
materials allows optical control of electronic, spin and valley degrees of
freedom, in which the structure of 2D materials is usually approximated to be
stationary with weak optical excitations. With increasing optical excitation
strengths, nonlinear processes start to occur Chernikov:2015gc ;
langer_lightwave-driven_2016 ; Rivera:2016ie  and the Born-Oppenheimer
approximation may not be applicable. In addition, toward the monolayer limit,
the influence of the surrounding environment on the properties of 2D systems
becomes increasingly important Sun:2017hf ; Nika:2012jv ; frigge2017 ;
Sun:2017hf . For example, the anomalously large thermal conductivity of
graphene may find applications in efficient thermal removal Balandin:2008fv ;
Ghosh:2010ja . Unconventional interface superconductivity is ascribed to the
unique electron-phonon coupling between the FeSe and the SrTiO3 interface
Lee:2014bw , and unusual exciton-phonon interactions have been observed across
the interface of vdW heterostructures as well as between monolayer
semiconductors and crystalline substrates Chow:2017jy ; jin_interlayer_2017 .
However, in contrast to many investigations that discover unique electronic,
spin, thermal, and optical properties of 2D materials and their interfaces,
limited knowledge of the associated structural dynamics has been obtained.
Understanding of these emergent phenomena in 2D systems beyond thin films
gerber_femtosecond_2017  calls for a direct quantitative measurement of the
lattice dynamics of monolayer crystals at and across crystalline interfaces on
ultrafast time scales.

Figure 1:  (A) A schematic diagram of femtosecond x-ray diffraction. The
specular $(00l)$ and the $(10l)$ rods are shown representatively across the
Ewald sphere. The X-ray probe beam strike on the sample close to grazing
incidence ($\alpha=1^{\circ}$) and the optical pump beam is overlap with the
x-ray beam with a horizontal crossing angle $\beta=5^{\circ}$. The inset shows
the optical images of the sample surface. Scale bar is 30 $\mu$m. (B) (center)
Corrected reciprocal space map around the off-specular $\\{10l\\}$ rod. (left)
Rod profiles for different $q_{z}$ (blue spots) and Gaussian fits (red), with
an offset that corresponds to the $q_{z}$ values. The dashed lines that
connect the curves at approximately their FWHM is drawn as a guide to the eye.
(right) Integrated intensity values for the ground state $\\{10l\\}$ CTR,
obtained by integration at different out-of-plane momentum transfer values
$q_{z}$.

With advances in generating ultrabright and ultrashort electron and x-ray
pulses, tracking atomic structural dynamics in 2D materials on femtosecond
time scales with high precision becomes possible. For example, ultrafast
electron diffraction (UED) and microscopy with large scattering cross section
allows measurements of transient structural changes in various multilayer
systems Raman:2008hb ; Lin:2017js ; waldecker:2017prl ;
cremons_femtosecond_2016 ; cremons_defect-mediated_2017  and at surfaces
ruan_ultrafast_PNAS2004 ; ruan_ultrafast_science_2004 ; frigge2017 . At the
monolayer limit, UED in a transmission geometry has been used to characterize
in-plane structural dynamics of monolayer 2D materials Mannebach:2015de ;
Hu:2016em , while the out-of-plane structural dynamics of a monolayer crystal
was only inferred Hu:2016em . Comparing with ultrafast electron diffraction,
ultrafast x-ray diffraction has been an indispensable tool for studying
structural dynamics in thin films, providing evidence on non-thermal
structural response in transition metal dichacogenides mannebach_dynamic_2017
and electron-phonon coupling in superconducting FeSe gerber_femtosecond_2017 .
In particular, ultrafast surface x-ray surface scattering can provide direct
and quantitative measurements of structural changes by recording diffraction
profile with non-zero momentum transfer along the out-of-plane direction, in
contrast to techniques that only measure in-plane diffraction peaks or surface
sensitive optical probes close to Brillouin zone center shen_phase-
sensitive_2013 . But the direct structural characterization of non-equilibrium
processes within a monolayer crystal remains a challenge due to significantly
reduced scattering volume. Ultrafast three-dimensional atomic-scale
rearrangements of monolayer crystals on supporting substrates, the most common
platform of 2D phenomena and configuration of 2D devices, have not yet been
mapped out.

In this article, we report the first femtosecond surface X-ray diffraction
(fSXD) study of monolayer crystals, which is enabled by the ultrahigh single-
pulse brightness and ultrashort pulse durations of hard x-ray radiation of
free electron lasers at the Linac Coherent Light Source (LCLS). Monolayer WSe2
is chosen as the model system because it hosts strong exciton-phonon coupling
with substantial impact in valley exciton dynamicsjones_excitonic_2016 ;
mishra_exciton-phonon_2018 , ultrafast dynamics poellmann_resonant_2015 ;
langer_lightwave-driven_2016 , unusual exciton- interfacial phonon
interactions at vdW interfaceChow:2017jy ; jin_interlayer_2017 , and unique
chiral phononszhu_observation_2018 , while its x-ray scattering cross section
is relatively large in the family of transition metal dichalcogenides. In
combination with crystallographic model-refinement calculations, we capture
the lattice motions of monolayer WSe2 along both in-plane and out-of-plane
directions upon optical excitation. In particular, we find direct structural
evidence of an anisotropic energy relaxation pathway that favors electron-
phonon coupling along the in-plane direction occurring on the time scale of 2
ps, subsequently followed by an in-plane lattice expansion. On the contrary,
the out-of-plane lattice vibration remains unchanged within the measurement
window of 10 ps. The strongly anisotropic response agrees with first-
principles simulation in real and momentum spaces, illuminating a key process
of anisotropic nonequilibrium lattice response in 2D materials. In addition,
the model assisted fitting suggests that the intralayer spacing change in
monolayers are asymmetric, in contrast to a symmetric intralayer compression
of bulk WSe2 on ps time scales, underlying a distinct structural response of
monolayer crystals on a supporting substrate. The demonstration of fSXD opens
opportunities to study nonequilibrium physics of monolayer crystals at
interfaces with atomic resolution on ultrafast time scales.

Figure 2:  (A) Time-dependent differential diffraction intensity as projected
to $q_{xy}$ axis integrated in the range $q_{z}=0.16-0.5$ Å-1. (B) The
differential diffraction intensity profile as a function of $q_{xy}$ before
and after optical excitation. (C) Time-dependent in-plane rod position shift
$\Delta q/q_{0}$ and diffraction intensity change $\Delta I/I_{0}$ of the
$\\{10L\\}$ reflection. The solid lines are fits presented in the text. The
error bars are the fitting errors.

### In-plane Structural Dynamics

We first characterize the sample at steady state by surface x-ray scattering
(Fig. 1A). The samples are WSe2 monolayer crystals with an averaged flake size
of a few $\mu m$ homogeneously covering the Al2O3 substrate (See Methods).
Since the crystal dimension is highly confined along the out-of-plane
direction, its Fourier transformation in the reciprocal space shows as a
vertical streak pattern along the crystal truncation rod (CTR) of a both-side
”truncated” crystal robinson_surface_1992  (See Methods). The in-plane random
orientations of WSe2 flakes permit recording the off-specular $\\{10l\\}$
crystal truncation rod (CTR), the sum of $(10l)$ and $(01l)$ rods, on the area
detector without rotating the sample, simultaneously measuring the diffraction
intensity distribution along the in-plane ($q_{xy}$) and out-of-plane
($q_{z}$) direction in reciprocal space. The in-plane intensity profile of
$\\{10l\\}$ rod is well fitted by a Gaussian shape with width increasing at
higher $q_{z}$, indicating rippling of the monolayer crystals (Fig. 1B)
Brivio:2011ch ; Meyer:2007kq .

The structural dynamics is measured by surface x-ray diffraction after optical
excitation with 650 nm light using pump-probe technique (See Methods). To
study the in-plane dynamics, we integrate the diffraction intensity along
$q_{z}$ in the range of $0.16-0.5\ \AA^{-1}$ (Fig. 1B) to obtain the
diffraction intensity profile projected onto the $q_{xy}$ axis. Time-dependent
intensity profiles are plotted as a function of delay in Fig. 2A. The
asymmetric wave-like differential profile after time zero (Fig. 2B) indicates
a diffraction intensity reduction and a rod position shift to lower $q_{xy}$
axis after excitation.

The $\\{10l\\}$ Bragg rod position and intensity can be extracted as a
function of time (Fig. 2C). Following optical excitation, we observe a
decrease in diffracted intensity as a result of Debye-Waller (DW) effect that
can be fit to an exponential function $\Delta I(t)\sim A[1-\exp(-t/\tau)]$
with amplitude $A$ and time constant $\tau$ (blue curves, Fig. 2C). The in-
plane electron-phonon coupling time $\tau=0.8\pm 0.4$ ps is faster than
$1.83\pm 0.13$ ps in bulk WSe2 waldecker:2017prl . The slowing down of energy
coupling to the in-plane lattice vibration in bulk may have multiple origins,
including lower defect density and indirect band gap in bulk, all of which can
reduce electron-phonon scattering rates and thus slow down the energy transfer
from electrons to in-plane lattice motion. The magnitude of $0.9\%$ reduction
of the diffraction intensity of $\\{10l\\}$ rods corresponds to $\Delta\langle
u_{xy}^{2}\rangle=[\ln(I_{0}/I)]/q_{xy}^{2}=0.0018\ \AA^{2}$, where $I_{0}$
and $I$ are the diffraction intensity before and after the excitation
Lin:2017js , and $\langle u_{xy}\rangle$ represents the root mean square
displacement (RMSD) along either $x$ or $y$ directions, assuming isotropic in-
plane atomic displacement. The increase of $\langle u_{xy}^{2}\rangle$
corresponds to an in-plane lattice temperature increase of $88$ K, consistent
with the estimated temperature rise from the absorbed energy (Supplementary
Note 3). The time-dependent change of the CTR position was determined by
fitting a 1D Gaussian profile to the $\\{10l\\}$ rod intensity as projected to
$q_{xy}$ axis. The peak position shifts as a function of time can be described
by an one-exponential function $\Delta q(t)\sim A[1-\exp(-t_{q}/\tau_{1})]$
(red curve, Fig. 2C). The time constant of $\tau_{1}=2.9\pm 1.2$ ps shows
characteristic time of the in-plane lattice expansion, as a result of an in-
plane acoustic wave propagation Hu:2016em ; Mannebach:2015de . Comparing with
the freestanding multilayer samples cremons_femtosecond_2016 ; cremons_defect-
mediated_2017 , the lack of oscillatory Bragg peak shift suggests an
overdamped mode that may result from the interaction with the substrate.

### Out-of-plane Structural Dynamics

Figure 3:  (A) Differential x-ray scattering intensity profile of WSe2
monolayers along the $\\{10l\\}$ rod for $5\leq\Delta t\leq 10$ ps. The solid
lines are model calculations discussed in the text. (B) Normalized in-plane
and out-of-plane RMSD of WSe2 monolayers. The error bars are the standard
deviation of the fitting parameters in all fitting trials. Solid curves are
the guides to the eye. (C) Schematic diagram of the atomic structure model of
monolayer WSe2. The blurriness of atom positions indicates the increase of the
in-plane RMSD. The red arrows show the possible intralayer distance changes.
(D) The diffraction intensity change of 004 Bragg peak of a bulk WSe2 crystal
upon optical excitation. The error bars show the standard errors of
consecutive scans. The inset shows the rocking curve with fits before and 5 ps
after optical excitation.

The out-of-plane lattice dynamics is obtained by comparing the measured CTRs
with crystallographic model-refinement calculations of the diffraction
intensity change along the $q_{z}$ as a function of time. The ground-state
$\\{10l\\}$ CTR is shown in (Fig. 1B). By subtracting the ground-state CTR
from the excited-state CTR recorded at each delay, the time-dependent
differential CTR along the $\\{10l\\}$ rod can be obtained. A representative
differential CTR is shown as circles in Fig. 3A. The differential intensity is
below zero, with a minimum change around $q_{z}=0.7$ Å-1, indicating a loss of
total diffraction intensity as a result of the increase of incoherent lattice
vibrations. To qualitatively understand the $q_{z}$ dependent differential
intensity profile, we compare the measured differenfial CTRs with calculated
ones with structural parameters including RMSDs of atoms and intralayer
spacings. The representative differential CTRs from four scenarios are shown
in Fig. 3A: the intralayer spacing expands (a) or contracts (b) by $0.2\%$
without RMSD increase; the out-of-plane (c) and in-plane (d) RMSD increase of
$12\%$ without d-spacing change. It is clear that only scenario d) matches the
data well, indicating that the energy relaxation is preferable along the in-
plane direction and symmetric intralayer d-spacing change does not agree with
the measurement. The magnitude of RMSD change and intralayer spacing change as
used in this simulation will be justified later. A systematical study of
differential CTRs as a function of various structural parameters can be found
in Supplementary Note 2.

Figure 4:  (A) The schematic of simulated system: WSe2 monolayer supported on
an Al2O3 substrate. (B) The in-plane and out-of-plane root mean squared
displacements of all atoms prior to and after electronic excitation
respectively. ”e-h” represents electron-hole injection at time zero with
carrier density of $2.6\times 10^{14}$ cm-2. The blue region represents the
coupling of the monolayer with the thermostat. (C) The intralayer spacing of
W-Se atomic planes before and after electronic excitation.

To quantify the RMSD increase as a function of time, least-squares fitting was
performed on the differential CTRs with the monolayer WSe2 structure
parameters allowed to vary (See Supplementary Note 1,2). Differential CTRs
were fit with two parameters, the percentage change of in-plane and out-of-
plane RMSD ($\sqrt{\langle u^{2}\rangle/\langle u_{0}^{2}\rangle}$), where
$\sqrt{\langle u^{2}\rangle}$ is the measured RMSD of the transient structure,
and $\sqrt{\langle u_{0}^{2}\rangle}$ is the calculated value for the ground
state (See Supplementary Note 4). The intralayer spacing change is neglected
for simplicity and will be treated in more details in the Discussion section.
From the model-based analysis of the x-ray scattering intensity profiles along
$\\{10l\\}$, we experimentally determined the corresponding mean square
displacements shown in Fig. 3B. Consistent with the qualitative analysis, the
out-of-plane RMSD remains almost the same within 10 ps, while the in-plane
RMSD increase $12\%$, corresponds to $0.007\ \AA$ increase of the in-plane
RMSD. The rise time is consistent with the blue curve in Fig. 2C, as expected.
This anomalous structural response is suggestive of a strong anisotropy of
energy relaxation pathways.

### First principles simulations

To give insight into the observed anisotropic energy relaxation pathway, we
first perform nonadiabatic quantum molecular dynamics (NAQMD) simulations
using the model shown in Fig. 4A. NAQMD follows the trajectories of all atoms,
while describing electronic excitations and nonadiabatic transitions between
excited electronic states assisted by atomic motions based on time-dependent
density functional theory and surface-hopping approaches, which enables it to
describe photoexcitation dynamics involving coupled motion of electrons and
nuclei Shimojo:2013hu .

Electronic excitation is simulated by the instantaneous creation of electron-
hole pairs in the monolayer-substrate simulation cell at time zero. Fig. 4B
show the calculated RMSD averaged over all atoms in the WSe2 monolayer as a
function of time at a simulated electron-hole concentration of 0 cm-2 (i.e. no
excitation) and $2.6\times 10^{14}$ cm-2 respectively. While the out-of-plane
RMSD remains close to 0.08 $\AA$ independent of excitation, the in-plane RMSD
increases strongly to over 0.3 $\AA$ approximately 300 fs after instantaneous
electronic excitation. The magnitude of the in-plane RMSD increase in the
simulation normalize to the electron density is in agreement of the measured
value since the excitation strength of simulated e-h density $2.6\times
10^{14}$ cm-2 is twenty times higher than that of $1.3\times 10^{13}$ cm-2
used in the experiments. We note that the in-plane lattice response relaxes to
the ground state within 1.5 ps due to the coupling of the WSe2 monolayer to
the Nose-Hoover thermostat at 300K. The use of Nose-Hoover thermostat is
required to stabilize the MD simulation. The coupling with the thermostat
unavoidably exaggerates the energy relaxation rate so that the relaxation of
RMSD occurs on an artificially fast time scale.

We note that the lateral size of WSe2 crystal of $<$ 1 nm in the NAQMD
simulation is much smaller than the rippling domain size of 10 nm so that the
nanoscale rippling effects are not taken into account. Complementary to NAQMD
simulations, we track phonon populations of all vibrational modes as a
function of time by calculating electron-phonon and third-order phonon-phonon
interactionssadasivam_theory_2017  (Supplementary Note 5). The rippling effect
is captured in these analytical calculations through the inclusion of
occupation of out-of-plane phonon modes, as shown by the larger out-of-plane
RMSD than the in-plane RMSD at the group state (Supplementary Note 4). The
excitation is simulated by a sudden electronic temperature jump at time zero
from 300 to 3000 K. The results shows a fast and significant increase of in-
plane RMSD within 1 ps but a slow and small rise of RMSD within 10 ps
(Supplementary Figure 2), consistent with the NAQMD simulations. The preferred
energy relaxation along the in-plane direction at short times after excitation
can be understood as the reduced density of out-of-plane phonon states in
monolayer crystalsataca_comparative_2011 .

## DISCUSSIONS

We now discuss the change of the intralayer spacing between W and Se atomic
planes within the monolayer upon optical excitation. We first present the bulk
response as a reference. The intralayer dynamics of an exfoliated, 50 nm-thick
WSe2 crystal was measured by monitoring 004 Bragg peak upon excitation of the
same 650 nm light pulses with an incident fluence of 9 mJ cm-2. We found the
diffraction peak intensity increases while the peak position does not shift
(Fig. 3D), indicating a dominant atomic motion within unit cell within 5 ps,
rather than unit cell size change that occurs at later time due to strain wave
propagation mannebach_dynamic_2017 , or the tilting of the sample. By
calculating the structure factor as a function of the intralayer spacing, the
diffraction intensity change of 8$\%$ corresponds to an intralayer contraction
of 1.4$\%$, which is 0.02 $\AA$ decrease of lattice spacing of W-Se layers.
The intralayer contraction agrees with the NAQMD simulation shown in Fig. 4C.
Assuming a linear dependence of the d-spacing change on the pump fluence, we
estimate a symmetric intralayer spacing change of 0.2$\%$ with the pump
fluence (1.5 mJ cm-2) used in the monolayer study.

The model-assisted fitting of differential CTR of monolayer crystals can yield
the intralayer spacings between W-Se layers if they are set as fitting
parameters during the fitting procedure. However, the fitting cannot converge
for non-zero symmetric intralayer spacing change that increase or decrease the
same amount. We then consider to model the intralayer spacing independently as
$d_{bot}$ and $d_{top}$, referring to the spacing between the top or bottom of
Se layers to the middle W layer (Fig. 3C). Based on the intralayer change in
the bulk, we constrain $\Delta d_{bot}$= 0.2$\%$. The fitting procedure
converges and yields $\Delta d_{top}$=-0.25$\pm 0.02\%$. The systematical
studies of the influence of structural parameters on differential CTRs show
that the asymmetric d-spacing change is required to fit the data, when
considering non-zero intralayer spacing change (Supplementary Note 2). This
indicates that the asymmetric infrared active mode $A^{{}^{\prime\prime}}_{2}$
is dominantly excited in monolayer crystals in contrast to the excitation of
the $A_{1g}$ mode in the bulkataca_comparative_2011 , which may be attributed
to the breaking of the mirror symmetry respect to W layers due to the
influence of substrate. The attempt to take account the substrate influence in
the NAQMD simulation by introducing one unit-cell-thick Al2O3 under WSe2 (Fig.
4A) does not show a significant asymmetric change of intralayer spacing (Fig.
4C), in comparison with the observed opposite sign change of intralayer
spacing. This is potentially due to the one-unit-cell-thick substrate in the
model. Simulations containing thicker substrates are computationally
challenging and beyond the scope of this work.

## Conclusions

We demonstrated the femtosecond surface x-ray diffraction to study
nonequilibrium structural dynamics of monolayer crystals on a supporting
substrate. Upon optical excitation, we characterized both in-plane and out-of-
plane atomic motions in monolayer WSe2 crystals. We found that energy
relaxation in lattice occurs anisotropically, favoring in-plane over out-of-
plane direction. The corresponding intralyer spacing change in monolayer
crystals are asymmetric, with Se atoms moving in the same direction respect to
W atoms, potentially due to the influence of the substrate, and is in contrast
to the symmetric intralayer lattice contraction in bulk crystals. These
measurements enable the direct comparison to nonadiabatic quantum molecular
dynamics simulations which largely reproduce the observations. Our general
understanding of ultrafast optoelectronic processes under intense optical
excitation need to be reevaluated to take into account the lattice degrees of
freedom. The demonstrated femtosecond surface x-ray diffraction advances x-ray
scattering technique for surface science on ultrafast time scales and opens
new opportunities for a direct characterization of lattice structure at and
across the interface of a wide range of low-dimensional material systems.

## Methods

### Sample Preparation and static surface x-ray diffraction

Monolayer WSe2 films used in this work were grown using a physical vapor
transport method Clark:2014fn  with the monolayer coverage over $95\%$ (grey
color, Fig. 1A inset) with a few mulilayer flakes $<3$ nm-thick (white color,
Fig. 1A inset). The small contribution from multilayer crystals does not alter
CTR profile and thus was not included in the model-assisted data analysis.
These crystals have an isotropic in-plane crystallite orientation
distribution. Figure 1A shows a schematic of the collinear pump-probe geometry
used in this study. A typical grazing-incidence diffraction pattern from
monolayer WSe2 on a sapphire substrate is shown on the flat area detector as a
tilted streaks in Fig. 1A. A data correction procedure Jiang:2015fn  is
applied to obtain diffraction intensity distribution in reciprocal space (Fig.
1B). Since the in-plane lattice constant of WSe2 is different from Al2O3
substrate, the monitored off-specular $\\{10l\\}$ CTR has no contribution from
the sapphire substrate, which allows independent analysis of the monolayer
structural properties without interference with the substrate Renaud:1998wt .
The $\\{10l\\}$ CTR of monolayer can then be discretely mapped by integrating
the corrected diffraction pattern (Fig. 1B) at different $q_{z}$ values
Mannsfeld:2009iy .

### Femtosecond surface X-ray Diffraction

Femtosecond x-ray scattering measurement were performed in grazing incident
geometry at the X-ray Pump-Probe (XPP) instrument at the Linac Coherent Light
Source (LCLS). The samples were kept under helium atmosphere during
measurements. The monochromatic X-ray beam with a photon energy of 9.55 keV
and 50 fs pulse duration strikes the sample surface at a grazing angle,
$\alpha=1^{\circ}$ shown in Fig. 1A. The large x-ray beam footprint resulting
from grazing incidence geometry also serves to spread the x-ray beam with the
cross section full-width-half-maxium of 50 $\times$ 50 $\mu m$ to minimize the
sample degradation. The diffracted intensity is then detected by a 2D area
detector, Cornell-SLAC Pixel Array Detector (CSPAD). The distance between
sample and detector is 431 mm, calibrated by LaB6 diffraction pattern. The
linearly polarized pump light pulses is derived from optical parametric
amplifier with the wavelength of 650 nm and 200 $\times$ 200 $\mu m$, close to
the absorption peak of the B-exciton of monolayer WSe2 Li:2014hd . Although
the incident fluence of 1.5 mJ cm-2 is relatively strong, the absorption of
optical energy in monolayer WSe2 only corresponds to an absorbed fluence of
6.2 $\mu$J cm-2, i.e., electron density of 1.3 $\times 10^{13}cm^{-1}$,
calculated based on the monolayer optical reflectivity and complex dielectric
constant Li:2014hd . The crossing angle between the laser and x-ray pulses is
5∘ in the horizontal plane while the x-ray scattering is in the vertical
plane. The temporal resolution is limited by the pump-probe timing jitter on
the order of 100 fs. The x-ray diffraction pattern are collected as a function
of pump-probe delay in a mode with laser-on and laser-off alternating at 60 Hz
repetition rate. The time-dependent reciprocal space maps are analyzed to
measure structural dynamics of the monolayer crystals. The sensitivity of the
measurement depends on sample quality, experimental geometry and signal-to-
noise ratio. Compared to the static measurements, the use of lock-in detection
in pump-probe measurements offers enhanced the sensitivity for measuring
relative change of the CTRs. In this study, the change of RMSD upon excitation
can be measured with an uncertainty of 0.002 $\AA$.

### Nonadiabatic quantum molecular dynamics simulations

Nonadiabatic quantum molecular dynamics (NAQMD) simulations were performed on
a simulation cell containing $3\times 3$ unit cells of WSe2 monolayer in the
2H crystal structure (9 formula units = 27 atoms) supported on a sapphire
(0001) surface. Simulations of free WSe2 monolayers were performed simulation
cells containing $3\times 3$ unit cells of WSe2 suspended in vacuum. All
simulations were performed using the highly-parallelized plane-wave DFT
program developed in-house, which can efficiently calculate long-range exact
exchange corrections and excited-state forces Shimojo:2014dt .

Electronic structures were described in the framework of density functional
theory (DFT) Hohenberg:1964zz ; Kohn:1965ui , and the generalized gradient
approximation was used for the exchange-correlation term Perdew:1996ug .
Valence wavefunctions are calculated by projector augmented-wave method
Blochl:1994uk , and projector functions were generated for the 4s, 4p and 4d
states of Selenium, 5d, 6s and 6p states of Tungsten, 3s, 3p and 3d states of
Aluminium, and 2s and 2p states of Oxygen respectively. The DFT-D method was
used to approximate van der Waals interactions in the system Grimme:2006fc .
The electronic pseudo-wave functions and pseudo-charge density were expanded
by plane waves with cut-off energies of 30 Ry and 250 Ry, respectively. All
NAQMD simulations were performed in the NVT ensemble with an external Nose-
Hoover thermostat at 300K and equations of motion are integrated with a time-
step of 0.97 fs.

###### Acknowledgements.

I.C.T., Q.Z., K.S., G.C., X. X., H.W. acknowledge the support from the
Department of Energy, Office of Science, Office of Basic Energy Sciences,
under Contract No. DE-SC0012509. AK, HK, AN, FS, RKK and PV acknowledge
support of the Computational Materials Sciences Program funded by the U.S.
Department of Energy, Office of Science, Basic Energy Sciences, under Award
Number DE-SC0014607. NAQMD simulations were performed at the Argonne
Leadership Computing Facility under the DOE INCITE program and at the Center
for High Performance Computing of the University of Southern California.Use of
the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory,
is supported by the U.S. Department of Energy, Office of Science, Office of
Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Work at the
Advanced Photon Source, Argonne was supported by the U.S. Department of
Energy, Office of Science under Grant No. DEAC02-06CH11357.

### Author contributions

I.C.T., H.Z., Q.Z., K.S., E.M., C.N., F.E., D.Z., J.G., M.K., S.S., X.X., A.M.
performed the measurements. A.K. H.K., F.S., R.K., R.V.,A.N., S.S., P.D. did
first-principle calculations. K.S., G.C., X.X. made samples. I.C.T. and H.W.
wrote the manuscript with contributions from all authors. H.W. and X.X.
conceived this study.

### Competing interests

The authors declare no competing interests.

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