arXiv subjects

Martin Eckstein

Publications and source records attributed to Martin Eckstein.

At least 73 records · Page 4Linked to original sources

arXiv2020

Manipulating intertwined orders in solids with quantum light

Intertwined orders exist ubiquitously in strongly correlated electronic systems and lead to intriguing phenomena in quantum materials. In this paper, we explore the unique opportunity of manipulating intertwined orders through entangling electronic states with quantum light. Using a quantum Floquet formalism to study the cavity-mediated interaction, we show the vacuum fluctuations effectively enhance the charge-density-wave correlation, giving rise to a phase with entangled electronic order and photon coherence, with putative superradiant behaviors in the thermodynamic limit. Furthermore, upon injecting even one single photon in the cavity, different orders, including $s$--wave and $η$--paired superconductivity, can be selectively enhanced. Our study suggests a new and generalisable pathway to control intertwined orders and create light-matter entanglement in quantum materials. The mechanism and methodology can be readily generalised to more complicated scenarios.

cond-mat.str-el↗

arXiv2020

Ultrafast dynamics in relativistic Mott insulators

We study the photoinduced ultrafast dynamics in relativistic Mott insulators, i.e., Mott insulators with strong spin-orbit coupling. For this purpose, we consider a minimal one-band Hubbard model on lattices with square and triangular symmetries, as relevant for layered transition metal compounds such as Sr$_2$IrO$_4$. Depending on the lattice and the spin-orbit coupling, the systems have canted antiferromagnetic or $120^\circ$ order. They are excited by simulating a short laser pulse, and the dynamics is solved using nonequilibrium dynamical mean-field theory. The pulse generates hot carriers, which subsequently perturb the magnetic order due to the coupling between the collective order and photocarriers. We find that this dynamics, which is known form regular antiferromagnets, depends sensitively on the spatial structure of the spin-orbit coupling. On the triangular lattice, in particular, relaxation times are influenced by the spin-orbit coupling for the chiral $120^\circ$ order, while on the square lattice with canted antiferromagnetic order the spin-orbit induced canting angle remains unchanged after the excitation. Our study opens up new possibilities of controlling magnetism and exotic spin states on the ultrafast timescales.

cond-mat.str-el↗

arXiv2020

A photo-induced strange metal with electron and hole quasi-particles

Photo-doping of Mott insulators or correlated metals can create an unusual metallic state which simultaneously hosts hole-like and electron-like particles. We study the dynamics of this state up to long times, as it passes its kinetic energy to the environment. When the system cools down, it crosses over from a bad metal into a resilient quasiparticle regime, in which quasiparticle bands are formed with separate Fermi levels for electrons and holes, but quasiparticles do not yet satisfy the Fermi liquid paradigm. Subsequently, the transfer of energy to the environment slows down significantly, and the system does not reach the Fermi liquid state even on the timescale of picoseconds. The transient photo-doped strange metal exhibits unusual properties of relevance for ultrafast charge and heat transport: In particular, there can be an asymmetry in the properties of electrons and holes, and strong correlations between electrons and holes, as seen in the spectral properties.

cond-mat.str-el↗

arXiv2020

$η$--paired superconducting hidden phase in photodoped Mott insulators

We show that a metastable $η$--pairing superconducting phase can be induced by photodoping doublons and holes into a strongly repulsive fermionic Hubbard model. The doublon-hole condensate originates from an intrinsic doublon-hole exchange interaction and does not rely on the symmetry of the half-filled Hubbard model. It extends over a wide range of doublon densities and effective temperatures. Different non-equilibrium protocols to realize this state are proposed and numerically tested. We also study the optical conductivity in the superconducting phase, which exhibits ideal metallic behavior, i.e., a delta function at zero-frequency in the conductivity, in conjunction with a negative conductivity at large frequencies. These characteristic optical properties can provide a fingerprint of the $η$-pairing phase in pump-probe experiments.

cond-mat.str-el↗

arXiv2020

Accelerated gap collapse in a Slater antiferromagnet

We study the melting of long-range antiferromagnetic order in the Hubbard model after an interaction quench, using non-equilibrium dynamical mean-field theory. From previous studies, the system is known to quickly relax into a prethermal symmetry-broken state. Using a convergent truncation of the memory integrals in the Kadanoff Baym equations, we unravel the subsequent relaxation dynamics of this state over several orders of magnitude in time. At long times, the prethermal state can be characterized by a single slow variable which is related to the conduction band population. The dynamics of this variable does not follow the paradigmatic steady relaxation of pre-thermal states: It is highly nonlinear, with a pronounced speedup once the gap falls below a certain value. This behavior indicates that non-thermal order can be self-stabilized on some timescale. It is not reproduced using simple Fermi's golden rule estimate for the evolution of the conduction band population.

cond-mat.str-el↗

arXiv2020

Nonequilibrium steady-state theory of photodoped Mott insulators

Photodoped states are widely observed in laser-excited Mott insulators, in which charge excitations are quickly created and can exist beyond the duration of the external driving. Despite the fruitful experimental explorations, theoretical studies on the microscopic models face the challenge to simultaneously deal with exponentially separated time scales, especially in multi-band systems, where the long-time behaviors are often well beyond the reach of state-of-the-art numerical tools. Here, we address this difficulty by introducing a steady-state description of photodoped Mott insulators using an open-system setup, where the photodoped system is stabilized as a non-equilirium steady-state (NESS) by a weak external driving. Taking advantage of the stationarity, we implement and discuss the details of an efficient numerical tool using the steady-state Dynamical Mean-Field Theory (DMFT), combined with the non-crossing approximation (NCA). We demonstrate that these stationary photodoped states exhibit the same properties of their transient counterparts, while being solvable with reasonable computational efforts. Furthermore, they can be parametrized by just few physical quantities, including the effective temperature and the density of charge excitations, which confirms the universal nature of photodoped states indeed independent of the excitation protocols. As a first application, we consider the stationary photodoped states in a two-band Hubbard model with intertwined spin-and-orbital ordering and find a family of hidden phases unknown from the previous studies, implying an apparently unexplored time regime of the relaxation of the intertwined orders.

cond-mat.str-el↗

arXiv2020

Electronic and fluctuation dynamics following a quench to the superconducting phase

We investigate the dynamics of superconducting fluctuations in the attractive three-dimensional Hubbard model after a quench from the disordered phase to the ordered regime. While the long time evolution is well understood in terms of dissipative time-dependent Ginzburg-Landau models with unstable potentials, early times are more demanding due to the inseparable dynamics of the pairing fluctuations and the electronic quasiparticles. Our simulation using the time-dependent fluctuation exchange approximation treat both degrees of freedom on the same footing and reveal a non-thermal electronic regime causing a non-monotonous growth of the fluctuations. This feature is not directly captured from the Ginzburg-Landau theory, but nevertheless remains observable beyond the thermalization time of the electrons. We further explore how the growth of the order parameter fluctuations leads to an opening of a pseudo-gap in the electronic spectrum, and identify Andreev reflections as the dominant mechanism behind the gap opening.

cond-mat.str-el↗

arXiv2020

Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium

We investigate out-of-equilibrium dynamics in an excitonic insulator (EI) with a finite momentum pairing perturbed by a laser-pulse excitation and a sudden coupling to fermionic baths. The transient dynamics of the excitonic order parameter is resolved using the full nonequilibrium Green's function approach and the generalized Kadanoff-Baym ansatz (GKBA) within the second-Born approximation. The comparison between the two approaches after a laser pulse excitation shows a good agreement in the weak and the intermediate photo-doping regime. In contrast, the laser-pulse dynamics resolved by the GKBA does not show a complete melting of the excitonic order after a strong excitation. Instead we observe persistent oscillations of the excitonic order parameter with a predominant frequency given by the renormalized equilibrium bandgap. This anomalous behavior can be overcome within the GKBA formalism by coupling to an external bath, which leads to a transition of the EI system towards the normal state. We analyze the long-time evolution of the system and distinguish decay timescales related to dephasing and thermalization.

cond-mat.str-el↗

arXiv2020

Quantum to classical crossover of Floquet engineering in correlated quantum systems

Light-matter coupling involving classical and quantum light offers a wide range of possibilities to tune the electronic properties of correlated quantum materials. Two paradigmatic results are the dynamical localization of electrons and the ultrafast control of spin dynamics, which have been discussed within classical Floquet engineering and in the deep quantum regime where vacuum fluctuations modify the properties of materials. Here we discuss how these two extreme limits are interpolated by a cavity which is driven to the excited states. In particular, this is achieved by formulating a Schrieffer-Wolff transformation for the cavity-coupled system, which is mathematically analogous to its Floquet counterpart. Some of the extraordinary results of Floquet-engineering, such as the sign reversal of the exchange interaction or electronic tunneling, which are not obtained by coupling to a dark cavity, can already be realized with a single-photon state (no coherent states are needed). The analytic results are verified and extended with numerical simulations on a two-site Hubbard model coupled to a driven cavity mode. Our results generalize the well-established Floquet-engineering of correlated electrons to the regime of quantum light. It opens up a new pathway of controlling properties of quantum materials with high tunability and low energy dissipation.

cond-mat.str-el↗

arXiv2020

Effects of frustration on the nonequilibrium dynamics of photo-excited lattice systems

We theoretically investigate the effects of the lattice geometry on the nonequilibrium dynamics of photo-excited carriers in a half-filled two-dimensional Hubbard model. Using a nonequilibrium generalization of the dynamical cluster approximation, we compare the relaxation dynamics in lattices which interpolate between the triangular lattice and square lattice configuration and thus reveal the role of the geometric frustration in these strongly correlated nonequilibrium systems. In particular, we show that the cooling effect resulting from the disordering of the spin background is less effective in the triangular case because of the frustration. This manifests itself in a longer relaxation time of the photo-doped population, as measured by the time-resolved photo-emission signal, and a higher effective temperature of the photo-doped carriers in the non-thermal steady state after the intra-Hubbard-band thermalization.

cond-mat.str-el↗

arXiv2020

Electromagnetic coupling in tight-binding models for strongly correlated light and matter

We discuss the construction of low-energy tight-binding Hamiltonians for condensed matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given set of Wannier orbitals. However, different representations of the continuum theory lead to different low-energy formulations, because different representations may entangle light and matter, transforming orbitals into light-matter hybrid states before the projection. In particular, a multi-center Power-Zienau-Woolley transformation yields a dipolar Hamiltonian which incorporates the light-matter coupling via both Peierls phases and a polarization density. We compare this dipolar gauge Hamiltonian and the straightforward Coulomb gauge Hamiltonian for a one-dimensional solid, to describe sub-cycle light-driven electronic motion in the semiclassical limit, and a coupling of the solid to a quantized cavity mode which renormalizes the band-structure into electron-polariton bands. Both descriptions yield the same result when many bands are taken into account, but the dipolar Hamiltonian is more accurate when the model is restricted to few electronic bands, while the Coulomb Hamiltonian requires fewer electromagnetic modes.

cond-mat.str-el↗

arXiv2020

Collective excitations of the U(1)-symmetric exciton insulator in a cavity

We investigate the equilibrium state and the collective modes of an excitonic insulator (EI) in a Fabry-Pérot cavity. In an EI, two bands of a semiconductor or semimetal spontaneously hybridize due to the Coulomb interaction between electrons and holes, leading to the opening of a gap. The coupling to the electromagnetic field reduces the symmetry of the system with respect to phase rotations of the excitonic order parameter from $U(1)$ to $Z_2$. While the reduction to a discrete symmetry would in general lead to a gapped phase mode and enhance the stability of the ordered phase, the coupling to the cavity leaves the mean-field ground state unaffected. Its energy remains invariant under $U(1)$ phase rotations, in spite of the lower $Z_2$ symmetry imposed by the cavity. In dipolar gauge, this can be traced back to the balancing of the linear light-matter coupling and the dipolar self-interaction at zero frequency. At nonzero frequency, however, the collective excitations do reflect the lower $Z_2$ symmetry, which shows that fluctuations beyond mean-field could play a crucial role in finding the true phase at finite temperature.

cond-mat.str-el↗

arXiv2020

Superconducting optical response of photodoped Mott insulators

Ultrafast laser pulses can redistribute charges in Mott insulators on extremely short time scales, leading to the fast generation of photocarriers. It has recently been demonstrated that these photocarriers can form a novel $η$--paired condensate at low temperatures, featuring a staggered superconducting pairing field. In this conference paper, we discuss the origin of the $η$--paired hidden phase and its optical response which may be detected in a pump-probe experiment. The hidden phase may be relevant for possible light-induced superconductivity in Mott insulators.

cond-mat.str-el↗

arXiv2019

Quantum Simulation Meets Nonequilibrium Dynamical Mean Field Theory: Exploring the Periodically Driven, Strongly Correlated Fermi-Hubbard Model

We perform an ab-initio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we find good agreement between experiment and theory, which cross-validates the experimental and numerical approaches in a strongly-correlated nonequilibrium system.

cond-mat.quant-gas↗

arXiv2019

Multi-band non-equilibrium GW+EDMFT formalism for correlated insulators

We study the dynamics of charge-transfer insulators after a photo-excitation using the three-band Emery model which is relevant for the description of cuprate superconductors. We provide a detailed derivation of the nonequilibrium extension of the multi-band GW+EDMFT formalism and the corresponding downfolding procedure. The Peierls construction of the electron-light coupling is generalized to the multi-band case resulting in a gauge invariant combination of the Peierls intra-band acceleration and dipolar intra-band transitions. We apply the formalism to the study of momentum-dependent (inverse) photo-emission spectra and optical conductivities. The time-resolved spectral function shows a strong renormalization of the charge-transfer gap and a substantial broadening of some of the bands. While the upper Hubbard band exhibits a momentum-dependent broadening, an almost rigid band shift is observed for the ligand bands. The inverse photo-emission spectrum reveals that the inclusion of the non-local and inter-band charge fluctuations lead to a very fast relaxation of holes into the lower Hubbard band. Consistent with the changes in the spectral function, the optical conductivity shows a renormalization of the charge-transfer gap, which is proportional to the photo-doping. The details of the photo-induced changes strongly depend on the dipolar matrix elements, which calls for an ab-initio determination of these parameters.

cond-mat.str-el↗

arXiv2019

Floquet DMFT Analysis of High Harmonic Generation in Mott Insulators

We study the high harmonic generation (HHG) in Mott insulators using Floquet dynamical mean-field theory (DMFT). We show that the main origin of the HHG in Mott insulators is the doublon-holon recombination, and that the character of the HHG spectrum differs depending on the field strength. In the weaker-field regime, the HHG spectrum shows a single plateau as in the HHG from gases, and its cut-off energy $ε_{\rm cut}$ scales linearly with the field strength $E_0$ as $ε_{\rm cut}=Δ_{\rm gap} + αE_0$, where $Δ_{\rm gap}$ is the Mott gap. On the other hand, in the stronger-field regime, multiple plateaus emerge and the $m$-th cut-off scales as $ε_{\rm cut,m}=U + m E_0$. We show that this difference originates from the different dynamics of the doublons and holons in the weak- and strong-field regimes. We also comment on the similarities and differences between HHG from Mott insulators and from semiconductors. This proceedings paper complements our recent work, Phys. Rev. Lett. 121, 057405 (2018), with additional results and analyses.

cond-mat.str-el↗

arXiv2019

NESSi: The Non-Equilibrium Systems Simulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump-probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green's functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. We present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green's functions on the L-shaped Kadanoff-Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green's functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green's functions. The library employs a discretization of the Kadanoff-Baym contour into time $N$ points and a high-order implementation of integration routines. The total integrated error scales up to $\mathcal{O}(N^{-7})$, which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers.

cs.CE↗

arXiv2019

Photo-enhanced excitonic correlations in a Mott insulator with nonlocal interactions

We investigate the effect of nonlocal interactions on the photo-doped Mott insulating state of the two-dimensional Hubbard model using a nonequilibrium generalization of the dynamical cluster approximation. In particular, we compare the situation where the excitonic states are lying within the continuum of doublon-holon excitations to a set-up where the excitons appear within the Mott gap. In the first case, the creation of nearest-neighbor doublon-holon pairs by excitations across the Mott gap results in enhanced excitonic correlations, but these excitons quickly decay into uncorrelated doublons and holons. In the second case, photo-excitation results in long-lived excitonic states. While in a low-temperature equilibrium state, excitonic features are usually not evident in single-particle observables such as the photoemission spectrum, we show that the photo-excited nonequilibrium system can exhibit in-gap states associated with the excitons. The comparison with exact-diagonalization results for small clusters allows us to identify the signatures of the excitons in the photo-emission spectrum.

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