Real-time quantum dynamics in photo-stimulated processes: experiment and theory
State of the art
On the experimental side, the time-resolved experimental techniques that are available to probe the transient electronic structure after excitation of charge carriers with light or intense pulsed laser fields have greatly been advanced during the last five years. Recent method developments include in particular the use of high-harmonic radiation in the water window for time-resolved X-ray spectroscopy [1,2]; the generation of bunches of attosecond electron pulses [3,4] and the development of new classes of ultrafast electron microscopes [5,6]; fundamental advances in 2D electronic spectroscopy by implementing ultrafast frequency comb light sources [7,8,9] and the development of new coherent and time-resolved scanning optical probe, scanning tunneling probe and single molecule spectroscopies [10-12].
One of the prominent research directions to be addressed by these methods aims at the spatio-temporal imaging of quantum dynamics in solid-state nanostructures. The achievable spatial and temporal resolution in new imaging approaches starts to exceed typical decoherence times and length scales of fundamental excitations, so that the tracking of coherent energy transfer and conversion processes in space and time is now within reach. First examples include the mapping of atom-selective electron-vibrational coupling within a single adsorbed molecule , the real-space tracking of coherent phonons and ordering dynamics during light-driven phase transitions [13,14].
This method development has also led to a series of studies of transient structural dynamics on ultrafast timescales, a particular challenge in the natural sciences. Alongside ultrafast X-ray techniques, time-resolved electron microscopy, diffraction and spectroscopy is developing into a more and more important tool, providing unprecedented insights into rapid physical, chemical and biological processes. The new Ultrafast Transmission Electron Microscopy ("UTEM"), developed by Schäfer and Ropers in Göttingen , has been employed to map the magnetization dynamics in permalloy disks with a spatial resolution of better than 100 nm and a time resolution of better than 1 ps . In this first demonstration of time-resolved Lorentz microscopy, the laser-induced demagnetization of a single magnetic vortex structure could be studied in space and time. The same group has advanced ultrafast low-energy electron diffraction by using metallic nantips as electron emitters. In a pioneering study they have employed this new technique to map the dynamics of phase ordering processes in charge density wave systems . In its present state of development, this UTEM provides an unprecedented combined spatio-temporal of 1 nm and 200 fs, respectively, offering fascinating new opportunities for space- and time-resolved probing of structural dynamics in nanostructures. In related work by the Miller group, ultrafast electron diffraction has been used to probe structurcal dynamics in photoexcited spin crossover crystals . Laser-induced electron diffraction has been used to disentangle electronic and nuclear motion in small photoexcited molecules in the gas phase .
In biological nanosystems, the role of quantum coherences for photosynthetic energy transport develops into a lively debated topic [19,20]. More and more groups are applying two-dimensional electronic spectroscopy to probe quantum coherences in light harvesting complexes or related model systems and to analyze their effects on excitonic energy transport phenomena [21,22]. The nature of the experimentally observed coherences is still under discussion. Even though it appears that experimental evidence is pointing towards a decisive role of vibronic quantum coherences, joined experimental-theoretical studies, using ab-initio methods and going beyond the use of model Hamiltonians seem imperative to settle this ongoing and important debate. Unambiguous experimental evidence has provided that strong vibronic coherences, persisting for hundreds of fs even at room temperature, drive light-induced charge transfer processes in organic semiconductors and photovoltaic materials [23,24]. This has stimulated an intense discussion about the role of those coherences for enhancing the efficiency of, e.g., organic solar cells . Quite generally, the ultrafast dynamics of electronic excitations in organic materials have been a topic of intense investigations. Charge migration in individual molecules has been studied using attosecond spectroscopy [26-28] and the intricate non-Born-Oppenheimer dynamics of vibronic wavepackets passing through conical intersections in multidimensional potential energy surfaces are beginning to emerge as a hot new topic [29,30]. Singlet fission dynamics have been explored in different organic systems as an technologically relevant example for the intricate spin dynamics in those materials [31,32].
Finally, the charge and energy transport dynamics in two different material systems, transition metal dichalcogenides (TMDs) as promising two-dimensional (2D) semiconductors for flexible optoelectronic, spintronic and photovoltaic devices and halide perovskites as a highly promising photovoltaic material, have attracted much interest. Early on, it was recognized that in many TMDC monolayers valley-selective carrier excitation can be induced by circularly polarized light. Furthermore, the pronounced electron-hole interaction in these materials results in rich physics of correlated electrons and holes states. The strong coupling of excitonic states to lattice distortions has resulted in the demonstration of single-photon emission from artificially strained TMDC monolayers . As a further control parameter, TMDC hetero bilayers were studied. Depending on the relative angular orientation and the unit cell dimensions of the individual TMDC layers, coupled excitonic states exist delocalized between the two layers. This has triggered important studies of the energy- and charge transfer dynamics in coupled multilayer systems . In addition, the lattice mismatch of the layers creates a nanometer-scale Moiré confinement potential, providing a hierarchy of length scales involved in electronic structure and dynamics and probably linking atomic-scale couplings with mesoscopic phenomena. In the related stacked 2D system of twisted graphene bilayers, it was already found that for certain stacking angles superconducting phases occur.
The intriguing and unusual optical properties of halide perovskites and their exceptionally high power conversion efficiencies in photovoltaic devices have triggered significant research efforts. Despite these efforts, however, the femtosecond dynamics of elementary optical excitations and in particular the coupling between electronic degrees of freedoms and phonon modes of the soft perovskite lattice are still debated. Over the past few years, first two-dimensional electronic spectroscopy studies of these materials have emerged [35-38], providing microscopic insight into exciton dissociation, charge carrier relaxation and many-body interactions in these materials. So far, however, the experimental results from different groups make quite different predictions for the dynamics charge carriers and their couplings to vibrational degrees of freedom. This not only calls for more in-depth experimental studies but in particular for a close experiment-theory collaboration to unravel the microscopic dynamics in this class of materials.
Summarizing, the advancement of time-resolved experimental techniques described above strongly demands to simultaneously advance the computational approaches to accurately model respective processes and understand the charge carrier dynamics and related transient phenomena on a fundamental level. Most fundamentally, there is an urgent need for ab-initio methods to tackle the challenging ultrafast, nano-scale charge, energy, and spin transport phenomena that lie at the heart of the function of natural and artificial nanostructures.
Theoretical studies on photo-physical and photochemical processes in nanoscale systems have been widely developed in the decades and will continue to be a topic of interest in forefronts of natural science. In addition to experimental science, computational modelling can provide important additional information inaccessible by experiment, and help us to understand different issues at molecular, atomic and even electronic levels of detail.
Recent progresses in electron-nuclear dynamics enable numerical simulations of complex ultrafast processes in the condensed phase. These advances have opened new avenues in the study of various photo-physical and photochemical processes triggered by the interaction with electromagnetic radiation. In particular, theoretical investigations can be combined with the most sophisticated femtosecond experimental techniques to guide the interpretation of measured time-resolved observables. At the same time, the availability of experimental data at high resolution, in both space and time, offers a unique opportunity for the benchmarking and improvement of the theoretical models used to describe complex molecular systems in their natural environment. The established synergy between theory and experiments can produce a better understanding of the ultrafast physical and chemical processes at the atomistic scale resolution. Furthermore, reliable ab initio molecular dynamics simulations can already be successful to predict and guide new experiments, as well as to design novel and more efficient materials. The aim is to describe the system of interest under the most realistic ambient conditions including all environmental effects that influence experiments, for instance, the interaction with the solvent and with an external time-dependent electric field.
To this end, time-dependent density functional theory (TD-DFT) is among the most efficient and accurate methods for the representation of the electronic dynamics, while nuclei move classically on the potential surface provided by the electrons. The semi-classical and mixed quantum-classical approaches include Tully’s surface hopping  and the mean-field non-adiabatic Ehrenfest dynamics [40,41]. Various group have successfully applied these methods to investigate solar cells , plasmonic nanoparticles , phase transitions , coherent electron-vibrational dynamics [coherent], chemical reactions and other processes. Most recently, these methods have been great improved and extended to describe the strong field effects in the non-perturbative regime in crystals using periodic boundary conditions [45-47]. These new developments allow information such as highly nonlinear optical responses , time-dependent high harmonic generation spectra  and time-resolved angle-resolved photoelectron emission (tr-ARPES) spectra  can be directly extracted from first-principles simulations, and be directly compared to experimental measurements towards the ultimate understanding of the microscopic mechanisms. The strong competition between different degrees of freedom in the physical systems under laser illumination, such as spin, orbital, lattice, and charge, and the correlation effects between interacting quantum particles, can be thus disentangled and clearly illustrated.
Theoretical studies of charge transport in nanoscale systems provide profound insights into the non-equilibrium processes involved in the photo-induced charge separation and migration. While the combined density functional theory (DFT) and non-equilibrium Green’s function (NEGF) approach has been widely employed to simulate steady state quantum electron transport through molecular junctions and other nanoscopic structures, the photo-induced processes require explicit time-domain simulations for direct comparison with advanced time-resolved experimental techniques. TD-DFT has been developed to study quantum transport phenomena [44-45]. As a formally rigorous and numerically tractable approach, TD-DFT promises real-time simulations on ultrafast electron transport through realistic electronic devices. By employing the NEGF approach and a partition-free scheme, Kurth, et al. derived the exact equations of motion for the two-time Green’s functions within TDDFT framework. They proposed a practical scheme in which the electronic wave-function is propagated in time domain that is subject to open boundaries . The resulting numerical method has been tested on model systems. Based on a reduced single-electron density matrix formulation, Zheng, et al. derived TD-DFT equations for open systems and applied them to realistic problems .
To cope with the increasing demand for renewable energy supply, solar cell research has become a hot topic within science and engineering. The need for higher solar cell efficiencies at a lower cost has become apparent. At the same time, synthetic control in nanoscience has improved such that high-performance electronic devices are now becoming possible. Nanowire solar cells have some potential benefits over traditional wafer-based or thin-film devices. Functioning nanowire photovoltaics have been fabricated using a wide variety of materials. Output efficiencies have steadily increased and have now achieved efficiencies close to 10%. At the same time, a number of unresolved questions must be answered before such materials can be used in commercial devices. Based on the NEGF formalism, Zhang, et al. modeled quantum mechanically the full I-V characteristics of a nanowire-based photovoltaic device . Organic photovoltaics show great promise owing to their synthetic variability, low temperature processing, and the possibility of producing lightweight, flexible, easily manufactured and inexpensive devices. However, the detailed mechanism of formation and dissociation of the charge transfer (CT) states is still controversial. Recently, a combined spectroscopic and non-adiabatic Ehrenfest dynamics study demonstrated a coherent ultrafast electron transfer between donor and acceptor in a prototype organic photovoltaic device . The electron dynamics with precise exciton binding energies between excited electrons and holes can now be treated based on GW approach based on time-dependent Bether-Salpeter equations [TDBSE].
Surface plasmons are collective oscillations of electrons that couple to electromagnetic fields, support intense electromagnetic field concentrations, and provide a pathway to couple optical energy from free space in nanoscale systems. Plasmons can decay either radiatively via emission of photons or non-radiatively through generation of excited carriers, referred to as hot carriers. Decay of surface plasmons to hot carriers finds a wide variety of applications in energy conversion, photocatalysis and photodetection. However, existing models fail to explain key quantitative details of the conversion of plasmons to hot carriers observed in experiments. Based on Fermi Golden’s rule and DFT calculations, Sundararaman, et al. report predictions for the prompt distributions of hot carriers generated by plasmon decay and find that carrier energy distributions are sensitive to the electronic band structure of the metal . Bernardi, et al. combine DFT, GW and electron phonon calculations to study the energy distribution and scattering processes for hot carriers generated by surface plasmons in noble metals. The calculations predict optimal conditions for hot carriers generation and extraction . Time domain simulations of Yu et al predict control of photochemical reactions and efficient photo-catalysis using plasmonic structures [plasmonics].
Molecules and materials under a periodic drive in time-domain emerges as a new area of optics and quantum physics, which are intrinsically connected to new concepts such Floquet band theory, far-from-equilibrium phenomena, time crystals etc [newconcept]. Combining first-principles electronic structure theory and the Floquet-Bloch theory analysis, the band structure of materials as well as their topological and optoelectronic structure under periodic laser illumination are subject to change in a controllable way, allowing for quantum engineering of material properties with very high tunability [floquet].
Chiyung Yam (Beijing Computational Science Research Center) - Organiser
Thomas Frauhenheim (Universität Bremen) - Organiser
Christoph Lienau (University Oldenburg, Germany) - Organiser