# Project B4

## 2017

### Probing the fluctuations of the optical properties in time-resolved spectroscopy

*F. Randi, M. Esposito, F. Giusti, F. Parmigiani, O. Misochko, D. Fausti, M. Eckstein*

We show that, in optical pump-probe experiments on bulk samples, the statistical distribution of the intensity of ultrashort light pulses after interaction with a nonequilibrium complex material can be used to measure the time-dependent noise of the current in the system. We illustrate the general arguments for a photoexcited Peierls material. The transient noise spectroscopy allows us to measure to what extent electronic degrees of freedom dynamically obey the fluctuation-dissipation theorem, and how well they thermalize during the coherent lattice vibrations. The proposed statistical measurement developed here provides a new general framework to retrieve dynamical information on the excited distributions in nonequilibrium experiments, which could be extended to other degrees of freedom of magnetic or vibrational origin.

### Nonequilibrium GW+EDMFT: Antiscreening and inverted populations from nonlocal correlations

*D. Golez, L. Boehnke, H. Strand, M. Eckstein, P. Werner*

We study the dynamics of screening in photodoped Mott insulators with long-ranged interactions using a nonequilibrium implementation of the *GW* plus extended dynamical mean-field theory formalism. Our study demonstrates that the complex interplay of the injected carriers with bosonic degrees of freedom (charge fluctuations) can result in long-lived transient states with properties that are distinctly different from those of thermal equilibrium states. Systems with strong nonlocal interactions are found to exhibit a self-sustained population inversion of the doublons and holes. This population inversion leads to low-energy antiscreening which can be detected in time-resolved electron-energy-loss spectra.

### Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

*Y. Murakami, N. Tsuji, M. Eckstein, P. Werner*

We perform a systematic analysis of the influence of phonon driving on the superconducting Holstein model coupled to heat baths by studying both the transient dynamics and the nonequilibrium steady state (NESS) in the weak and strong electron-phonon coupling regimes. Our study is based on the nonequilibrium dynamical mean-field theory, and for the NESS we present a Floquet formulation adapted to electron-phonon systems. The analysis of the phonon propagator suggests that the effective attractive interaction can be strongly enhanced in a parametric resonant regime because of the Floquet side bands of phonons. While this may be expected to enhance the superconductivity (SC), our fully self-consistent calculations, which include the effects of heating and nonthermal distributions, show that the parametric phonon driving generically results in a suppression or complete melting of the SC order. In the strong coupling regime, the NESS always shows a suppression of the SC gap, the SC order parameter, and the superfluid density as a result of the driving, and this tendency is most prominent at the parametric resonance. Using the real-time nonequilibrium DMFT formalism, we also study the dynamics towards the NESS, which shows that the heating effect dominates the transient dynamics, and SC is weakened by the external driving, in particular at the parametric resonance. In the weak coupling regime, we find that the SC fluctuations above the transition temperature are generally weakened under the driving. The strongest suppression occurs again around the parametric resonances because of the efficient energy absorption.

## 2016

### Slowdown of the Electronic Relaxation Close to the Mott Transition

*Sharareh Sayyad and Martin Eckstein*

We investigate the time-dependent reformation of the quasiparticle peak in a correlated metal near the Mott transition, after the system is quenched into a hot electron state and equilibrates with an environment which is colder than the Fermi-liquid crossover temperature. Close to the transition, we identify a purely electronic bottleneck time scale, which depends on the spectral weight around the Fermi energy in the bad metallic phase in a nonlinear way. This time scale can be orders of magnitude larger than the bare and renormalized electronic hopping time, so that a separation of electronic and lattice time scales may break down. The results are obtained using nonequilibrium dynamical mean-field theory and a slave-rotor representation of the Anderson impurity model.

### Versatile approach to spin dynamics in correlated electron systems

*Malte Behrmann, Alexander I. Lichtenstein, Mikhail I. Katsnelson, and Frank Lechermann*

Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner-Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However, many experimental studies, e.g., of (de)magnetization processes, focus on itinerant local-moment materials, such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space implementation of the time-dependent rotational-invariant slave boson methodology allows us to treat nonequilibrium spins numerically fast and efficiently beyond linear response as well as beyond the band-theoretical or Heisenberg limit.

### Nonequilibrium itinerant-electron magnetism: a time-dependent mean-field theory

*A. Secchi, A. I. Lichtenstein, and M. I. Katsnelson*

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

### Photo-induced gap closure in an excitonic insulator

*D. Golež, P. Werner, M. Eckstein*

We study the dynamical phase transition out of an excitonic insulator phase after photoexcitation using a time-dependent extension of the self-consistent GW method. We connect the evolution of the photoemission spectra to the dynamics of the excitonic order parameter and identify two dynamical phase transition points marked by a slowdown in the relaxation: one critical point is connected with the trapping in a nonthermal state with reduced exciton density and the second corresponds to the thermal phase transition. The transfer of kinetic energy from the photoexcited carriers to the exciton condensate is shown to be the main mechanism for the gap melting. We analyze the low energy dynamics of screening, which strongly depends on the presence of the excitonic gap, and argue that it is difficult to interpret the static component of the screened interaction as the effective interaction of some low energy model. Instead we propose a phenomenological measure for the effective interaction which indicates that screening has minor effects on the low energy dynamics.

### Nonequilibrium self-energy functional approach to the dynamical Mott transition

*F. Hofmann, M. Eckstein, M. Potthoff*

The real-time dynamics of the Fermi-Hubbard model, driven out of equilibrium by quenching or ramping the interaction parameter, is studied within the framework of the nonequilibrium self-energy functional theory. A dynamical impurity approximation with a single auxiliary bath site is considered as a reference system and the time-dependent hybridization is optimized as prescribed by the variational principle. The dynamical two-site approximation turns out to be useful to study the real-time dynamics on short and intermediate time scales. Depending on the strength of the interaction in the final state, two qualitatively different response regimes are found. For both weak and strong couplings, qualitative agreement with previous results of nonequilibrium dynamical mean-field theory is found. The two regimes are sharply separated by a critical point at which the low-energy bath degree of freedom decouples in the course of time. We trace the dependence of the critical interaction of the dynamical Mott transition on the duration of the interaction ramp from sudden quenches to adiabatic dynamics, and therewith link the dynamical to the equilibrium Mott transition.

### Non-equilibrium variational-cluster approach to real-time dynamics in the Fermi-Hubbard model

*Felix Hofmann, Martin Eckstein, Michael Potthoff*

The non-equilibrium variational-cluster approach is applied to study the real-time dynamics of the double occupancy in the one-dimensional Fermi-Hubbard model after different fast changes of hopping parameters. A simple reference system, consisting of isolated Hubbard dimers, is used to discuss different aspects of the numerical implementation of the approach in the general framework of non-equilibrium self-energy functional theory. Opposed to a direct solution of the Euler equation, its time derivative is found to serve as numerically tractable and stable conditional equation to fix the time-dependent variational parameters.

Journal of Physics: Conference Series, Volume 696, conference 1

## 2015

### Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

*Isabella Gierz, Matteo Mitrano, Hubertus Bromberger, Cephise Cacho, Richard Chapman, Emma Springate, Stefan Link, Ulrich Starke, Burkhard Sachs, Martin Eckstein, Tim O. Wehling, Mikhail I. Katsnelson, Alexander Lichtenstein, and Andrea Cavalleri*

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane *E _{1u}* lattice vibration at 6.3

*μ*m. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the

*K*point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the

*E*vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

_{1u}### Large-amplitude spin oscillations triggered by nonequilibrium strongly correlated t2g electrons

*M. Behrmann, F. Lechermann*

Laser-induced ultrafast (fs) magnetization experiments in antiferromagnets have recently attracted large attention, paving the road for inherently fast spin dynamics in the THz regime without invoking stray fields. The technical importance is emphasized by the rising new research field of antiferromagnetic (AFM) spintronics, where superexchange-dominated strongly correlated compounds provide an interesting materials playground. An intriguing question is whether the Coulomb interaction may be a key to control AFM order on ultrafast time scales. Therefore, we study (de)magnetization processes in a time-dependent multiorbital Hubbard model, focusing on t2g electrons in a wider doping range. Depending on filling, we reveal large-amplitude spin oscillations via interaction quenches from the antiferromagnetic or paramagnetic state. Nonequilibrium ultrafast spin-orientation effects in prominent correlated transition-metal oxides are therefrom predicted.

Phys. Rev. B 91, 075110 (2015)

## 2014

### Fermi Condensation Near van Hove Singularities Within the Hubbard Model on the Triangular Lattice

*D. Yudin, D. Hirschmeier, H. Hafermann, O. Eriksson, A. I. Lichtenstein, M. I. Katsnelson*

The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands (“Fermi condensation”) within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1–0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.

Phys. Rev. Lett. 112, 070403 (2014)

## 2013

### Extended dynamic Mott transition in the two-band Hubbard model out of equilibrium

*M. Behrmann, M. Fabrizio, F. Lechermann*

We reformulate the time-dependent Gutzwiller approximation by M. Schiró and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.

Phys. Rev. B 88, 035116 (2013)

### Non-equilibrium magnetic interactions in strongly correlated systems

*A. Secchi, S. Brener, A. I. Lichtenstein, M. I. Katsnelson*

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii–Moriya coupling, but is not due to spin–orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

Ann. Phys. 333, 221 (2013)

## 2012

### Competing orders in Na_xCoO_2 from strong correlations on a two-particle level

*L. Boehnke, F. Lechermann*

Based on dynamical mean-field theory with a continuous-time quantum Monte-Carlo impurity solver, static as well as dynamic spin and charge susceptibilites for the phase diagram of the sodium cobaltate system Na$_x$CoO$_2$ are discussed. The approach includes important vertex contributions to the q-dependent two-particle response functions by means of a local approximation to the irreducible vertex function in the particle-hole channel. A single-band Hubbard model suffices to reveal several charge- and spin-instability tendencies in accordance with experiment, including the stabilization of an effective kagome sublattice close to x=0.67, without invoking the doping-dependent Na-potential landscape. The in-plane antiferromagnetic-to-ferromagnetic crossover is additionally verified by means of the computed Korringa ratio. Moreover an intricate high-energy mode in the transverse spin susceptiblity is revealed, pointing towards a strong energy dependence of the effective intersite exchange.

Phys. Rev. B 85, 115128 (2012)

http://arxiv.org/abs/1012.5943