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Theory of ultra-fast dynamics in correlated multi-band systems

Periodic Reporting for period 4 - UfastU (Theory of ultra-fast dynamics in correlated multi-band systems)

Reporting period: 2021-10-01 to 2022-09-30

Pump-probe experiments with femtosecond laser pulses allow to study solids on the intrinsic timescale of their microscopic constituents, and have opened an entirely new direction of research in condensed matter physics. Of particular interest in this context are strongly correlated materials, in which the collective behavior of many particles gives rise to emergent phenomena like magnetism, high-temperature superconductivity, and interaction-induced metal-insulator transitions. Seminal experiments, such as the observation of light-induced superconductivity, have given a first glance at the largely unexplored non-equilibrium phase diagrams in such systems. A full access to this terrain would both answer fundamental questions of many-body physics and it may bring about new concepts for quantum technological applications.

The project UfastU succeeded to develop new computational tools to describe the light-induced dynamics in particular in correlated materials whose behavior is determined by more than one active orbital. The starting point was dynamical mean-field theory (DMFT), which is nowadays one of the most widely used approaches to describe the electronic structure whenever conventional density functional theory fails. UfastU developed extensions of DMFT which can address the real-time dynamics, and which fully include how microscopic interactions like the Coulomb repulsion between electrons are influenced by the laser excitation. The methodology was used to predict pathways for the controlled laser manipulation of solids, including an electronic mechanism to reach a so-called hidden state with intertwined magnetic and orbital order, and mechanism for photo-induced superconductivity. Moreover, one branch of UfastU explored the theoretical foundation of quantum electrodynamics in condensed matter, and could therefore show how the quantum nature of confined modes of the electromagnetic field (e.g. plasmonic modes) can affect properties of matter in a similar manner as classical laser excitation.
Within UfastU, we developed theoretical concepts and methods to understand the control of quantum materials with out-of-equilibrium protocols:

Nonlinear phononics: An intriguing pathway of materials control is non-linear phononics, where the coherent excitation of a phonon is used to modify a material on time average. Along these lines, we predicted a metal-insulator transition driven by a coherent phonon [Phys. Rev. B 103, L041110 (2021)]. A key novel aspect of this study was to show the importance of the quantum dynamics of the phonon in this context.

Photo-doping and hidden quantum states: Changing the electron filling (“chemical doping”) is one of the most versatile ways to control material properties. It is therefore an interesting question whether a similar control can be reached on the ultrafast timescale by photo-doping, i.e. by transferring electrons between different bands. Using our (in part) newly developed methodology to simulate photo-doping in correlated systems, we discovered a novel pathway to switch a material to a so-called hidden state with orbital and magnetic order that is inaccessible through conventional thermodynamic pathways [Nature Comm. 9, 4581 (2018)]. Moreover we devised a protocol in which the photo-doping process itself leads to cooling [Nature Comm.10 5556 (2019)], thus reaching phases which can potentially host exotic hidden states. With this we could demonstrate, e.g. that a photo-doped Mott insulator can host a non-equilibrium superconducting phase in a wide parameter regime [Phys. Rev. B 102, 165136 (2020)].

Electronic structure of photo-doped states: In order to accurately describe light-induced dynamics, it is essential to understand how the interaction itself, which eventually governs the collective behavior of the solid, is modified. To address this question, we have established the multi-band non-equilibrium GW+EDMFT framework [Phys. Rev. B 100, 235117 (2019)]. This was used to predict the electronic structure of the most paradigmatic charge transfer insulator, consistently including lifetime changes of the electronic quasiparticles, photo-induced band shifts, and a dynamical modification of the interaction parameters. Such changes are now becoming experimentally accessible through Xray absorption spectroscopy based on new generation spectrometers at Xray free electron lasers. The novel method also provides the basis for a first-principles description of correlated electron systems out of equilibrium.

Quantum light-matter hybrids: This line of research was motivated by striking experimental findings that demonstrated a possible enhancement of collective properties of matter by coupling to confined modes of the electromagnetic field in a cavity. We provided a concise derivation of effective low energy tight-binding models which includes the strong coupling to the electromagnetic field. This formed the basis for several subsequent findings, including a prediction how quantum light can control competing phases [Phys. Rev. Lett. 125, 217402 (2020)], a microscopic theory for the cavity control of a ferroelectric transition, or a proposal for the cavity control of so called Shiba states, which may be used for quantum state manipulations [arXiv:2207.14180 Phys. Rev. Lett.]

Advances in non-equilibrium Green’s function techniques: Non-equilibrium Green’s function (NEGF) techniques provide the basis for an unbiased theoretical description of the electron dynamics in solids. However, the numerical effort for NEGF simulations scales with the third power of the total simulated time, making many interesting physical regimes inaccessible. We have implemented a way to reduce the numerical effort to a linear scaling, which allowed us to reach up to two orders of magnitude longer times in some simulations. We have also published a fully documented open source code NESSi for NEGF simulations ( which has been presented already at international research summer schools.

Semiclassical stochastic approach: The most recent method development forms the basis for combined simulation of electron and lattice dynamics, which can be considered as a stochastic molecular dynamics simulation for strongly correlated electron systems such as Mott insulators (arxiv:2209.00428). Since the lattice dynamics is of crucial importance for the understanding of many photo-induced phase transitions, we expect this methodology to be used in future applications.
Within UfastU a methodology was developed which can simulate the dynamics of correlated electrons in a way that goes beyond the state of the art in non-equilibrium simulations in three mayor aspects: (i), the formalism can efficiently include more than one active orbital and thus address realistic models for a large class of correlated materials, (ii), a formalism was developed to include the dynamical modification of the interaction, which turned out to be essential in order to fully capture laser-induced modifications of the electronic structure, and (iii), a framework was set up for simulations of the combined electron-lattice dynamics within dynamical mean-field theory. Beyond the specific results listed in the description of the work, these developments should further help to enable first-principle simulations of controlled dynamical processes in condensed matter, such as laser-induced phase transitions.
Multi-orbital systems have complex phase diagrams with many intertwined electronic orders. We try to

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