Complete collisions approximation to the Kadanoff-Baym equation: a first-principles implementation

Time-Dependent Screening Explains the Ultrafast Excitonic Signal Rise in 2D Semiconductors

We calculate the time evolution of the transient reflection signal in an MoS₂ monolayer on a SiO₂/Si substrate using first-principles out-of-equilibrium real-time methods. Our simulations provide a simple and intuitive physical picture for the delayed, yet ultrafast, evolution of the signal whose rise time depends on the excess energy of the pump laser: at laser energies above the A- and B-exciton, the pump pulse excites electrons and holes far away from the K valleys in the first Brillouin zone. Electron-phonon and hole-phonon scattering lead to a gradual relaxation of the carriers toward small Active Excitonic Regions around K, enhancing the dielectric screening. The accompanying time-dependent band gap renormalization dominates over Pauli blocking and the excitonic binding energy renormalization. This explains the delayed buildup of the transient reflection signal of the probe pulse, in excellent agreement with recent experimental data. Our results show that the observed delay is not a unique signature of an exciton formation process but rather caused by coordinated carrier dynamics and its influence on the screening.

Ultrafast dynamics of strongly correlated fermions-nonequilibrium Green functions and selfenergy approximations

This article presents an overview on recent progress in the theory of nonequilibrium Green functions (NEGF). We discuss applications of NEGF simulations to describe the femtosecond dynamics of various finite fermionic systems following an excitation out of equilibrium. This includes the expansion dynamics of ultracold atoms in optical lattices following a confinement quench and the excitation of strongly correlated electrons in a solid by the impact of a charged particle. NEGF, presently, are the only ab initio quantum approach that is able to study the dynamics of correlations for long times in two and three dimensions. However, until recently, NEGF simulations have mostly been performed with rather simple selfenergy approximations such as the second-order Born approximation (SOA). While they correctly capture the qualitative trends of the relaxation towards equilibrium, the reliability and accuracy of these NEGF simulations has remained open, for a long time. Here we report on recent tests of NEGF simulations for finite lattice systems against exact-diagonalization and density-matrix-renormalization-group benchmark data. The results confirm the high accuracy and predictive capability of NEGF simulations-provided selfenergies are used that go beyond the SOA and adequately include strong correlation and dynamical-screening effects. With an extended arsenal of selfenergies that can be used effectively, the NEGF approach has the potential of becoming a powerful simulation tool with broad areas of new applications including strongly correlated solids and ultracold atoms. The present review aims at making such applications possible. To this end we present a selfcontained introduction to the theory of NEGF and give an overview on recent numerical applications to compute the ultrafast relaxation dynamics of correlated fermions. In the second part we give a detailed introduction to selfenergies beyond the SOA. Important examples are the third-order approximation, the [Formula: see text] approximation, the T-matrix approximation and the fluctuating-exchange approximation. We give a comprehensive summary of the explicit selfenergy expressions for a variety of systems of practical relevance, starting from the most general expressions (general basis) and the Feynman diagrams, and including also the important cases of diagonal basis sets, the Hubbard model and the differences occuring for bosons and fermions. With these details, and information on the computational effort and scaling with the basis size and propagation duration, readers will be able to choose the proper basis set and straightforwardly implement and apply advanced selfenergy approximations to a broad class of systems.

Intravalley Spin-Flip Relaxation Dynamics in Single-Layer WS2

In monolayer (1L) transition metal dichalcogenides (TMDs) the valence and conduction bands are spin-split because of the strong spin-orbit interaction. In tungsten-based TMDs the spin-ordering of the conduction band is such that the so-called dark excitons, consisting of electrons and holes with opposite spin orientation, have lower energy than A excitons. The transition from bright to dark excitons involves the scattering of electrons from the upper to the lower conduction band at the K point of the Brillouin zone, with detrimental effects for the optoelectronic response of 1L-TMDs, since this reduces their light emission efficiency. Here, we exploit the valley selective optical selection rules and use two-color helicity-resolved pump-probe spectroscopy to directly measure the intravalley spin-flip relaxation dynamics in 1L-WS₂. This occurs on a sub-ps time scale, and it is significantly dependent on temperature, indicative of phonon-assisted relaxation. Time-dependent ab initio calculations show that intravalley spin-flip scattering occurs on significantly longer time scales only at the K point, while the occupation of states away from the minimum of the conduction band significantly reduces the scattering time. Our results shed light on the scattering processes determining the light emission efficiency in optoelectronic and photonic devices based on 1L-TMDs.

Ab Initio Calculations of Ultrashort Carrier Dynamics in Two-Dimensional Materials: Valley Depolarization in Single-Layer WSe2

In single-layer WSe₂, a paradigmatic semiconducting transition metal dichalcogenide, a circularly polarized laser field can selectively excite electronic transitions in one of the inequivalent K^± valleys. Such selective valley population corresponds to a pseudospin polarization. This can be used as a degree of freedom in a "valleytronic" device provided that the time scale for its depolarization is sufficiently large. Yet, the mechanism behind the valley depolarization still remains heavily debated. Recent time-dependent Kerr experiments have provided an accurate way to visualize the valley dynamics by measuring the rotation of a linearly polarized probe pulse applied after a circularly polarized pump pulse. We present here a clear, accurate and parameter-free description of the valley dynamics. By using an atomistic, ab initio approach, we fully disclose the elemental mechanisms that dictate the depolarization effects. Our results are in excellent agreement with recent time-dependent Kerr experiments. We explain the Kerr dynamics and its temperature dependence in terms of electron-phonon-mediated processes that induce spin-flip intervalley transitions.

Photo-Induced Bandgap Renormalization Governs the Ultrafast Response of Single-Layer MoS2

Transition metal dichalcogenides (TMDs) are emerging as promising two-dimensional (2D) semiconductors for optoelectronic and flexible devices. However, a microscopic explanation of their photophysics, of pivotal importance for the understanding and optimization of device operation, is still lacking. Here, we use femtosecond transient absorption spectroscopy, with pump pulse tunability and broadband probing, to monitor the relaxation dynamics of single-layer MoS2 over the entire visible range, upon photoexcitation of different excitonic transitions. We find that, irrespective of excitation photon energy, the transient absorption spectrum shows the simultaneous bleaching of all excitonic transitions and corresponding red-shifted photoinduced absorption bands. First-principle modeling of the ultrafast optical response reveals that a transient bandgap renormalization, caused by the presence of photoexcited carriers, is primarily responsible for the observed features. Our results demonstrate the strong impact of many-body effects in the transient optical response of TMDs even in the low-excitation-density regime.