Ultrafast electron diffuse scattering as a tool for studying phonon transport: Phonon hydrodynamics and second sound oscillations.

Hydrodynamic phonon transport phenomena, like second sound, have been observed in liquid helium more than 50 years ago. More recently second sound has been observed in graphite at over 200 K using transient thermal grating (TG) techniques. In this work, we explore signatures of phonon hydrodynamic transport and second sound oscillations in ultrafast electron diffuse scattering patterns, which can provide time, momentum, and branch resolved information on the state-of-excitation of the phonon system beyond that available through TG experiments. We use the density functional theory and solve the Boltzmann transport equation to determine time-resolved non-equilibrium phonon populations and model phonon transport in graphite. This model also provides the information necessary to calculate the time evolution of one-phonon structure factors and diffuse scattering patterns during thermal transport covering ballistic, diffusive, and hydrodynamic regimes where the effect of a second sound oscillation on the phonon distribution is observed. Direct measurements of how the phonon distribution varies in time and space in various thermal transport regimes should yield new insights into the fundamental physics of the underlying processes.

Direct View of Phonon Dynamics in Atomically Thin MoS2.

Transition-metal dichalcogenide monolayers and heterostructures are highly tunable material systems that provide excellent models for physical phenomena at the two-dimensional (2D) limit. While most studies to date have focused on electrons and electron-hole pairs, phonons also play essential roles. Here, we apply ultrafast electron diffraction and diffuse scattering to directly quantify, with time and momentum resolution, electron-phonon coupling (EPC) in monolayer molybdenum disulfide and phonon transport from the monolayer to a silicon nitride substrate. Optically generated hot carriers result in a profoundly anisotropic distribution of phonons in the monolayer within ∼5 ps. A quantitative comparison with ab initio ultrafast dynamics simulations reveals the essential role of dielectric screening in weakening EPC. Thermal transport from the monolayer to the substrate occurs with the phonon system far from equilibrium. While screening in 2D is known to strongly affect equilibrium properties, our findings extend this understanding to the dynamic regime.

Direct visualization of polaron formation in the thermoelectric SnSe.

SnSe is a layered material that currently holds the record for bulk thermoelectric efficiency. The primary determinant of this high efficiency is thought to be the anomalously low thermal conductivity resulting from strong anharmonic coupling within the phonon system. Here we show that the nature of the carrier system in SnSe is also determined by strong coupling to phonons by directly visualizing polaron formation in the material. We employ ultrafast electron diffraction and diffuse scattering to track the response of phonons in both momentum and time to the photodoping of free carriers across the bandgap, observing the bimodal and anisotropic lattice distortions that drive carrier localization. Relatively large (18.7 Å), quasi-one-dimensional (1D) polarons are formed on the 300-fs timescale with smaller (4.2 Å) 3D polarons taking an order of magnitude longer (4 ps) to form. This difference appears to be a consequence of the profoundly anisotropic electron-phonon coupling in SnSe, with strong Fröhlich coupling only to zone-center polar optical phonons. These results demonstrate a high density of polarons in SnSe at optimal doping levels. Strong electron-phonon coupling is critical to the thermoelectric performance of this benchmark material and, potentially, high performance thermoelectrics more generally.

Revealing momentum-dependent electron-phonon and phonon-phonon coupling in complex materials with ultrafast electron diffuse scattering.

ABSTRACT: Despite their fundamental role in determining many important properties of materials, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling across the entire Brillouin zone has remained elusive. Ultrafast electron diffuse scattering (UEDS) is a recently developed technique that is making a significant contribution to these questions. Here, we describe both the UEDS methodology and the information content of ultrafast, photoinduced changes in phonon-diffuse scattering from single-crystal materials. We present results obtained from Ni, WSe2, and TiSe2, materials that are characterized by a complex interplay between electronic (charge, spin) and lattice degrees of freedom. We demonstrate the power of this technique by unraveling carrier-phonon and phonon-phonon interactions in both momentum and time and following nonequilibrium phonon dynamics in detail on ultrafast time scales. By combining ab initio calculations with ultrafast diffuse electron scattering, insights into electronic and magnetic dynamics that impact UEDS indirectly can also be obtained.

Mechanisms of electron-phonon coupling unraveled in momentum and time: The case of soft phonons in TiSe2.

The complex coupling between charge carriers and phonons is responsible for diverse phenomena in condensed matter. We apply ultrafast electron diffuse scattering to unravel electron-phonon coupling phenomena in 1T-TiSe2 in both momentum and time. We are able to distinguish effects due to the real part of the many-body bare electronic susceptibility, [Formula: see text], from those due to the electron-phonon coupling vertex, g q , by following the response of semimetallic (normal-phase) 1T-TiSe2 to the selective photo-doping of carriers into the electron pocket at the Fermi level. Quasi-impulsive and wave vector-specific renormalization of soft zone-boundary phonon frequencies (stiffening) is observed, followed by wave vector-independent electron-phonon equilibration. These results unravel the underlying mechanisms driving the phonon softening that is associated with the charge density wave transition at lower temperatures.

How optical excitation controls the structure and properties of vanadium dioxide.

We combine ultrafast electron diffraction and time-resolved terahertz spectroscopy measurements to link structure and electronic transport properties during the photoinduced insulator-metal transitions in vanadium dioxide. We determine the structure of the metastable monoclinic metal phase, which exhibits antiferroelectric charge order arising from a thermally activated, orbital-selective phase transition in the electron system. The relative contribution of the photoinduced monoclinic and rutile metals to the time-dependent and pump-fluence-dependent multiphase character of the film is established, as is the respective impact of these two distinct phase transitions on the observed changes in terahertz conductivity. Our results represent an important example of how light can control the properties of strongly correlated materials and demonstrate that multimodal experiments are essential when seeking a detailed connection between ultrafast changes in optical-electronic properties and lattice structure.

An open-source software ecosystem for the interactive exploration of ultrafast electron scattering data.

This paper details a software ecosystem comprising three free and open-source Python packages for processing raw ultrafast electron scattering (UES) data and interactively exploring the processed data. The first package, iris, is graphical user-interface program and library for interactive exploration of UES data. Under the hood, iris makes use of npstreams, an extensions of numpy to streaming array-processing, for high-throughput parallel data reduction. Finally, we present scikit-ued, a library of reusable routines and data structures for analysis of UES data, including specialized image processing algorithms, simulation routines, and crystal structure manipulation operations. In this paper, some of the features or all three packages are highlighted, such as parallel data reduction, image registration, interactive exploration. The packages are fully tested and documented and are released under permissive licenses.

A general method for baseline-removal in ultrafast electron powder diffraction data using the dual-tree complex wavelet transform.

The general problem of background subtraction in ultrafast electron powder diffraction (UEPD) is presented with a focus on the diffraction patterns obtained from materials of moderately complex structure which contain many overlapping peaks and effectively no scattering vector regions that can be considered exclusively background. We compare the performance of background subtraction algorithms based on discrete and dual-tree complex (DTCWT) wavelet transforms when applied to simulated UEPD data on the M1-R phase transition in VO2 with a time-varying background. We find that the DTCWT approach is capable of extracting intensities that are accurate to better than 2% across the whole range of scattering vector simulated, effectively independent of delay time. A Python package is available.

Coherent and incoherent electron-phonon coupling in graphite observed with radio-frequency compressed ultrafast electron diffraction.

Radio-frequency compressed ultrafast electron diffraction has been used to probe the coherent and incoherent coupling of impulsive electronic excitation at 1.55 eV (800 nm) to optical and acoustic phonon modes directly from the perspective of the lattice degrees of freedom. A biexponential suppression of diffracted intensity due to relaxation of the electronic system into incoherent phonons is observed, with the 250 fs fast contribution dominated by coupling to the E_{2g2} optical phonon mode at the Γ point (Γ-E_{2g2}) and A_{1}^{'} optical phonon mode at the K point (K-A_{1}^{'}). Both modes have Kohn anomalies at these points in the Brillouin zone. The result is a unique nonequilibrium state with the electron subsystem in thermal equilibrium with only a very small subset of the lattice degrees of freedom within 500 fs following photoexcitation. This state relaxes through further electron-phonon and phonon-phonon pathways on the 6.5 ps time scale. In addition, electronic excitation leads to both in-plane and out-of-plane coherent lattice responses in graphite whose character we are able to fully determine based on spot positions and intensity modulations in the femtosecond electron diffraction data. The in-plane motion is specifically a Γ point shearing mode of the graphene planes and the out-of-plane motion an acoustic breathing mode response of the film.

A photoinduced metal-like phase of monoclinic VO2 revealed by ultrafast electron diffraction.

The complex interplay among several active degrees of freedom (charge, lattice, orbital, and spin) is thought to determine the electronic properties of many oxides. We report on combined ultrafast electron diffraction and infrared transmissivity experiments in which we directly monitored and separated the lattice and charge density reorganizations that are associated with the optically induced semiconductor-metal transition in vanadium dioxide (VO2). By photoexciting the monoclinic semiconducting phase, we were able to induce a transition to a metastable state that retained the periodic lattice distortion characteristic of the semiconductor but also acquired metal-like mid-infrared optical properties. Our results demonstrate that ultrafast electron diffraction is capable of following details of both lattice and electronic structural dynamics on the ultrafast time scale.

Donor-Bridge-Acceptor Proton Transfer in Aqueous Solution.

We use ab initio molecular dynamics to study proton transfer in a donor-bridge-acceptor system in which the bridge is a single water molecule and the entire system is embedded in aqueous solution. The results, based on a large number of proton transfer trajectories, demonstrate that the dominant charge-transfer pathway is a subpicosecond "through bridge" event in which the bridge adopts an Eigen-like (hydronium) structure. We also identify another state in which the bridge forms a Zundel-like configuration with the acceptor that appears to be a dead end for the charge transfer. The reaction coordinate is inherently multidimensional and, as we demonstrate, cannot be given in terms of either local structural parameters of the donor-bridge-acceptor system or local solvent coordination numbers.

Direct optical measurements of the evolving spatio-temporal charge density in ultrashort electron pulses.

The temporal evolution of the charge density distribution in femtosecond laser produced electron pulses was studied using electron-laser pulse cross correlation techniques and compared to analytical predictions and simulations. The influence of propagation time and weak magnetic focusing were both investigated. Our results show that ultrashort electron pulses develop a relatively uniform internal charge density as they propagate, which is in good agreement with analytical predictions, and that weakly focusing an ultrashort electron pulse results in an increased internal charge density towards the leading edge of the pulse.

Concerted and Sequential Proton Transfer Mechanisms in Water-Separated Acid-Base Encounter Pairs.

The proton transfer mechanisms involved inside aqueous, solvent-separated encounter complexes between phenol and carboxyl moieties are studied using ab initio molecular dynamics and computational time-resolved vibrational spectroscopy. This model framework can be viewed as a ground-state analog of the excited-state proton transfer reactions that have been actively investigated using ultrafast spectroscopy. Three qualitatively distinct proton transfer pathways are observed in the simulations. These can be described as direct concerted, direct sequential, and through bulk transfers. The primary difference between the sequential and concerted mechanism is the involvement of a reaction intermediate in which the proton fluctuates for several picoseconds through the hydrogen bonds connecting donor and acceptor but resides primarily on an intervening water molecule in the encounter complex. These results contribute to our molecular level understanding of the diverse processes involved in proton transfer within water-separated encounter complexes.

Influence of ions on aqueous acid-base reactions.

We study the effects of bromide salts on the rate and mechanism of the aqueous proton/deuteron-transfer reaction between the photoacid 8-hydroxy-1,3,6-pyrenetrisulfonic acid (HPTS) and the base acetate. The proton/deuteron release is triggered by exciting HPTS with 400 nm femtosecond laser pulses. Probing the electronic and vibrational resonances of the photoacid, the conjugate photobase, the hydrated proton/deuteron and the accepting base with femtosecond visible and mid-infrared pulses monitors the proton transfer. Two reaction channels are identified: 1) direct long-range proton transfer over hydrogen-bonded water bridges that connect the acid and base and 2) acid dissociation to produce fully solvated protons followed by proton scavenging from solution by acetate. We observe that the addition of salt affects the long-range reaction pathway, and reduces both the rate at which protons are released to solution by HPTS and the rate at which solvated protons are scavenged from solution by acetate. We study the dependence of these effects on the nature and concentration of the dissolved salt.

On the role of water in intermolecular proton-transfer reactions.

We study the mechanism of proton transfer (PT) between the photoacid (8-hydroxy-1,3,6-pyrenetrisulfonic acid (HPTS)) and the base acetate in aqueous solution using femtosecond vibrational spectroscopy. By probing the vibrational resonances of the photoacid, the accepting base, and the hydrated proton we find that intermolecular PT in this model system involves the transfer of the proton across several water molecules linking the donor-acceptor pair by hydrogen bonds (H-bonds). We find that at high base concentration the rate of PT is not determined by the mutual diffusion of acid and base but rather by the rate of Grotthuss-like conduction of the proton between molecules. This long-range PT requires an activated solvent configuration to facilitate the charge transfer.

Characterization of ultrashort electron pulses by electron-laser pulse cross correlation.

An all-optical method to determine the duration of ultrashort electron pulses is presented. This technique makes use of the laser pulse ponderomotive potential to effectively sample the temporal envelope of the electron pulse by sequentially scattering different sections of the pulse out of the main beam. Using laser pulse parameters that are easily accessible with modern tabletop chirped-pulse amplification laser sources, it is possible to measure the instantaneous duration of electron pulses shorter than 100 fs in the energy range that is most useful for electron diffraction studies, 10-300 keV.

An atomic-level view of melting using femtosecond electron diffraction.

We used 600-femtosecond electron pulses to study the structural evolution of aluminum as it underwent an ultrafast laser-induced solid-liquid phase transition. Real-time observations showed the loss of long-range order that was present in the crystalline phase and the emergence of the liquid structure where only short-range atomic correlations were present; this transition occurred in 3.5 picoseconds for thin-film aluminum with an excitation fluence of 70 millijoules per square centimeter. The sensitivity and time resolution were sufficient to capture the time-dependent pair correlation function as the system evolved from the solid to the liquid state. These observations provide an atomic-level description of the melting process, in which the dynamics are best understood as a thermal phase transition under strongly driven conditions.