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arXiv:1610.07246 · Physical review. B./Physical review. B

Relaxation of photoexcitations in polaron-induced magnetic microstructures

Thomas Köhler, Sangeeta Rajpurohit, Ole Schumann, Sebastian Paeckel, Fabian Biebl, Mohsen Sotoudeh, Stephan C. Kramer, Peter E. Blöchl, Stefan K. Kehrein, Salvatore R. Manmana

Published Jun 12, 2018• 9 citations
arXivHTMLPDF

Abstract

We investigate the evolution of a photoexcitation in correlated materials over a wide range of time scales. The system studied is a one-dimensional model of a manganite with correlated electron, spin, orbital, and lattice degrees of freedom, which we relate to the three-dimensional material ${\mathrm{Pr}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$. The ground-state phases for the entire composition range are determined and rationalized by a coarse-grained polaron model. At half doping a pattern of antiferromagnetically coupled Zener polarons is realized. Using time-dependent density-matrix renormalization group (tDMRG), we treat the electronic quantum dynamics following the excitation. The emergence of quasiparticles is addressed, and the relaxation of the nonequilibrium quasiparticle distribution is investigated via a linearized quantum-Boltzmann equation. Our approach shows that the magnetic microstructure caused by the Zener polarons leads to an increase of the relaxation times of the excitation.

DOI
10.1103/physrevb.97.235120

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We investigate the evolution of a photoexcitation in correlated materials over a wide range of time scales. The system studied is a one-dimensional model of a manganite with correlated electron, spin, orbital, and lattice degrees of freedom, which we relate to the three-dimensional material Pr1\ensuremath−xCaxMnO3{\mathrm{Pr}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}Pr1\ensuremath−x​Cax​MnO3​. The ground-state phases for the entire composition range are determined and rationalized by a coarse-grained polaron model. At half doping a pattern of antiferromagnetically coupled Zener polarons is realized. Using time-dependent density-matrix renormalization group (tDMRG), we treat the electronic quantum dynamics following the excitation. The emergence of quasiparticles is addressed, and the relaxation of the nonequilibrium quasiparticle distribution is investigated via a linearized quantum-Boltzmann equation. Our approach shows that the magnetic microstructure caused by the Zener polarons leads to an increase of the relaxation times of the excitation.
We investigate the behavior of 1D correlated systems following a photo-excitation by combining ab-initio methods, time-dependent matrix product state (MPS) approaches, analytical insights from quantum Boltzmann equations, and molecular dynamics (MD) simulations to describe the dynamics on different time scales ranging from femtoseconds up to nanoseconds. This is done for manganite systems in the material class Pr1−xCaxMnO3. We derive one-dimensional ab-initio model Hamiltonians for which we compute the ground states at different values of the doping using MD simulations. At half doping, we obtain a magnetic microstructure of alternating dimers which we use as a starting point to formulate a one-dimensional Hubbard-type model. In this strongly correlated 1D system we address the formation of quasiparticles after photoexcitations. We introduce a quasiclassical model for the absorption process of light which takes into account the backaction of the electrons to the electromagnetic field and compare the results with the ones obtained with a Peierls substitution ansatz in which we neglect the backaction. Taking this effect into account leads to a stronger response since the emitted radiation can be re-absorbed by neighboring particles. We use the resulting state as starting point for the short-time dynamics which we obtain from 'numerically exact' MPS calculations. The dynamics is analyzed concerning the formation and lifetime of quasi-particles which form a starting point for the description of the relaxation process via a linearized quantum Boltzmann equation. In this way, our work constitutes a first step to building a unifying theoretical framework for the description of photoexcitations in strongly correlated materials over a wide range of time scales, capable of making predictions for ongoing experiments investigating pump-probe situations and unconventional photovoltaics.
The emergence of order in materials with strongly-correlated electrons in out-of-equilibrium situations inspires a lot of new research, both experimental and theoretical. The main goal of this theoretical research project is to better understand related questions in the dynamics in a strongly correlated many-body state after a photoexcitation has occured. Such situations are usually not fully explainable in a mean-field picture nor analytically solvable. Hence, advanced numerical techniques are necessary. In this work, we investigate non-equilib- rium situations after photoexcitations. In order to model a hypothetical one-dimensional (1D) manganite, we chose the 1D Hubbard model with nearest-neighbor interaction and a staggered magnetic field. The photoexcitation is modeled in two different ways: First we investigate sud- den, local excitations, and afterwards we study a semi-classical approach by applying the Peierls substitution, which leads to a time-dependent Hamiltonian. All simulations are performed with an implementation of the time-dependent density-matrix renormalization group (DMRG), which is formulated by tensor-network states (TNSs), namely matrix-product states (MPSs) and matrix-product operators (MPOs). The framework used offers the possibility that every MPO can be externally described by finite-state machines (FSMs), hence it is extremely flexible. In this thesis, we explain how to perform exact FSM arithmetics, and how to compress the resulting FSMs. Based on MPSs and FSMs, a quantum-computer simulator (QCS) is introduced, which is mainly used as a universal tool for (MPS)-quantum- state manipulations. From the investigations with the sudden, local excitations, we learned that the electron-electron interaction is responsible for a rapid relaxation of the magnetic moment of the individual bands. Nevertheless, this relaxation can be stalled via a stronger magnetic microstructure. By applying a spin-selective photoexcitation via the Peierls substitution, we are able to induce a meta-stable charge-density wave (CDW) pattern if a magnetic microstructure is present. For a small, but finite interaction, we find a decay channel for the doublon-based part of the CDW, which still leaves a finite pattern. For large interaction, nearly no doublons are created by the photoexcitation. In the opposite limit, i.e., the non-interacting case, the two spin species are decoupled. Hence, in both limits the decay channel does not weaken the CDW and we find the pattern to be stable up to the times we can treat.
We study the ultrafast dynamic process in photoexcited systems and find that the Franck-Condon or Landau-Zener tunneling between the photoexcited state and the ground state is abruptly blocked with increasing the state coupling from nonadiabatic to adiabatic limits. The blockage of the tunneling inhibits the photoexcited state from decaying into the thermalized state and results in an emergence of a metastable state, which represents an entanglement of electronic states with different electron-phonon coupling strengths. Applying this model to the investigation of photoexcited half-doped manganites, we show that the quantum critical transition is responsible for more than a three-order-of-magnitude difference in the ground-state recovery times following photoirradiation. This model also explains some elusive experimental results, such as photoinduced rearrangement of orbital order by the structural rather than electronic process and the structural bottleneck of a one-quarter period of the Jahn-Teller mode. We demonstrate that in the spin-boson model there exist unexplored regions not covered in the conventional phase diagram.
We consider a one-dimensional Hund lattice model where a conducting band is coupled with localized spins s = 1/2 interacting antiferromagnetically, with coupling constant J , and investigate the ground state phase diagram as a function of both the exchange coupling J and the band filling, n . From spin structure factor measurements we found different evolving magnetic orderings in the ground state related to the particle distribution in the systems, although no charge density waves are formed, as found from density-density correlation function measurements. We study the quasiparticle formation and phase separation using the density-matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.
Quantum materials are systems in which electronic ground states emerge from strong interactions between charge, spin, lattice, and orbital degrees of freedom. These interactions may be enhanced by reduced dimensionality or geometric frustration, and may also result in topologically protected electronic states. Noninteracting single band models fail to adequately describe these systems. Time-resolved optical measurements using femtosecond laser pulses can be used to study strongly interacting degrees of freedom on their natural timescales. By photoexciting the samples gently, it is possible to study these dynamics without disturbing the underlying order. In this work, the relaxation dynamics of photoexcited quasiparticles are studied in several quantum materials in which Coulomb repulsion and spin-orbit coupling are both strong. The relaxation dynamics reveal information about the low energy energy electronic structure as well as the nature of the strong interactions that govern the emergent properties of the system.
Using a nonequilibrium implementation of the extended dynamical mean-field theory (EDMFT) we simulate the relaxation after photoexcitation in a strongly correlated electron system with antiferromagnetic spin interactions. We consider the $t\ensuremath{-}J$ model and focus on the interplay between the charge and spin dynamics in different excitation and doping regimes. The appearance of string states after a weak photoexcitation manifests itself in a nontrivial scaling of the relaxation time with the exchange coupling and leads to a correlated oscillatory evolution of the kinetic energy and spin-spin correlation function. A strong excitation of the system, on the other hand, suppresses the spin correlations and results in a relaxation that is controlled by hole scattering. We discuss the possibility of detecting string states in optical and cold-atom experiments.