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

Periodic Reporting for period 2 - UfastU (Theory of ultra-fast dynamics in correlated multi-band systems)

Reporting period: 2018-10-01 to 2020-03-31

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 in the field of 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 such as magnetism, high-temperature superconductivity, or interaction- induced metal-insulator transitions. Seminal experiments, including the finding of light-induced superconductivity and photo-induced transitions to hidden phases in materials with highly entangled orbital, spin, and lattice degrees of freedom show that the rich equilibrium phase diagrams in correlated systems are most certainly complemented by an equally rich but unexplored manifold of non-equilibrium states. An access to this terrain would not only answer fundamental questions of many-body physics, but it may also bring about new concepts for technological applications such as femtosecond switches and optically controlled magnetic memory, or lead to a better understanding of transport processes in photovoltaic devices.

The remarkable experimental progress is contrasted by a rather limited theoretical understanding of non-equilibrium processes in correlated systems. Most microscopic theory has been based on single-band models with ad-hoc parameters, while many of the emergent phenomena in correlated materials are intimately connected to the presence of more than one active degree of freedom. Our central objective is thus to develop a versatile computational tool which can describe correlated multi- band systems with dynamic interactions and help to identify new ways to manipulate their cooperative behavior far from equilibrium. With this, we would like to lay the foundations for an ab-initio approach to the real-time dynamics of correlated materials based on the dynamical mean-field theory (DMFT) and its extensions. This methodological advance would, e.g. open the possibility to understand light-induced superconductivity in multi-orbital materials such as iron pnictides or doped fullerenes.
We have done research along domain lines, i.e. (1) non-equilibrium dynamics in complex materials with intertwined and competing orders, and (2), the study of electronic structure of complex materials out of equilibrium.Exemplary results are presented below:

(1) We have further developed a formalism (the multi-orbital strong-coupling expansion for dynamical mean-field theory) which allows to theoretically address the non-equilibrium physics of complex oxide materials (photo-induced states and steady states driven by a strong current). Using this technique, we could study the paradigmatic model for a Mott insulator with intertwined spin and orbital order (KCuF), and could reveal an entirely new mechanism for switching to so called-hidden states, i.e. states which have no equilibrium counterpart [Li et al., Nature Communications 9, 4581 (2018)]. The mechanism relies on a non-thermal partial melting of the intertwined orders mediated by photoinduced charge excitations in the presence of strong spin-orbital exchange interactions. Our study theoretically confirms the crucial role played by orbital degrees of freedom in the light-induced dynamics of strongly correlated materials and it shows that the switching to hidden states can be controlled already on the femtosecond timescale of the electron dynamics.

(2) In collaboration with researchers at the University of Fribourg, we further developed a theoretical formalism (non-equilibrium GW+DMFT) which allows to include dynamical screening and multi-bands effects into the description of the electronic structure out of equilibrium [Golez et al., arXiv:1808.02264]. This allowed us for the first time to reveal both static and dynamic band-shifts and broadenings in the band structure of photo-excited materials. In future, one can extend this formalism, which currently only covers the short (femtosecond ) dynamics, to study longer times, using an extension of a quantum Boltzmann approach that resulted out of another collaboration [Wais et al. Phys. Rev. B 98, 134312 (2018)].
We wish to

(1) arrive at the first stage of an ab-initio description for the electronic structure in complex materials out of equilibrium, in analogy to the combination of density functional theory and dynamical mean-field theory which is state of the art for the description of equilibrium properties in complex solids.

(2) unravel novel mechanisms for driving ultra-fast transitions between different non-equilibrium phases, including superconductivity, magnetic order, charge density waves, or orbital order.
Multi-orbital systems have complex phase diagrams with many intertwined electronic orders. We try to