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arXiv:0907.0945 · Journal of Physics Conference Series

Photoinduced insulator-metal transition and nonlinear optical response of correlated electrons – a DMFT analysis

N Tsuji, T Oka, H Aoki

Published Feb 1, 2009• 0 citations
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Abstract

We investigate a photoinduced insulator-metal transition in the Falicov-Kimball model with the dynamical mean-field theory (DMFT) extended to nonequilibrium systems in periodic modulations in time. When the photon energy of the pump light is Ω≈ ( U : the interaction strength), a Drude-like peak is found to grow in the optical conductivity spectrum, which is an evidence that the system is driven into a metallic state. During the transition, the band gap does not collapse, whereas the distribution function exhibits a non-monotonic behaviour away from the Fermi distribution. This indicates that the transition cannot be accounted for by heating effects, but creation of photo-carriers is responsible.

DOI
10.1088/1742-6596/148/1/012058

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We investigate a photoinduced insulator-metal transition in the Falicov-Kimball model with the dynamical mean-field theory (DMFT) extended to nonequilibrium systems in periodic modulations in time. When the photon energy of the pump light is Ω≈ ( U : the interaction strength), a Drude-like peak is found to grow in the optical conductivity spectrum, which is an evidence that the system is driven into a metallic state. During the transition, the band gap does not collapse, whereas the distribution function exhibits a non-monotonic behaviour away from the Fermi distribution. This indicates that the transition cannot be accounted for by heating effects, but creation of photo-carriers is responsible.
To reveal the nature of the photoinduced insulator-metal transition, we show that an exact analysis of the Falicov-Kimball model subject to external ac electric fields becomes possible with Floquet's method combined with the nonequilibrium dynamical mean-field theory. The nonequilibrium steady state that appears during irradiation of a pump light is shown to be determined if the dissipation in a certain heat-bath model is introduced. This has enabled us to predict that novel features characteristic of the photoexcited steady states, i.e., negative weight (gain) in the low-energy region and dip structures around the photon energy of the pump light, should be observed in the optical conductivity. Special emphasis is put on the role of dissipation, for which we elaborate the dependence of the steady state on the strength of dissipation and the temperature of the heat bath.
In order to investigate photoinduced insulator-metal transitions observed in correlated electron systems, we propose a new theoretical method, where we combine a Floquet-matrix method for AC-driven systems with the dynamical mean-field theory. The method can treat nonequilibrium steady states exactly beyond the linear-response regime. We have applied the method to the Falicov-Kimball model coupled to AC electric fields, and numerically obtained the spectral function, the nonequilibrium distribution function and the current-voltage characteristic. The results show that intense AC fields indeed drive Mott-like insulating states into photoinduced metallic states in a nonlinear way.
We propose to combine the Floquet formalism for systems in ac fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively include both the correlation effects and nonlinear effects due to the driving field, which is imperative in analyzing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single-band noninteracting systems. As a demonstration, we have applied the method to the Falicov-Kimball model in intense ac fields to calculate the spectral function. The result shows that photoinduced midgap states emerge from strong ac fields, triggering an insulator-metal transition.
Utilizing the exact diagonalization method, we investigate the one-dimensional Peierls-Hubbard model at quarter filling, where it manifests as an antiferromagnetic Mott insulator in units of dimers. By increasing the on-site Coulomb repulsion UUU, we observe a significant suppression of the Drude peak, based on a nonequilibrium linear-response theory capable of capturing the zero-frequency (Drude) weight of the optical conductivity under periodic boundary conditions. However, after the ultrafast photoirradiation of this model with large UUU, we detect a distinct enhancement of the Drude peak, signifying the onset of a photoinduced insulator-metal transition. Comparing these dynamics with the half-filled Hubbard model and a noninteracting spinless half-filled Su-Schrieffer-Heeger model (corresponding to the quarter-filled Peierls-Hubbard model with infinite UUU), we propose a mechanism for the photoinduced metallic state: The empty-occupied and double-occupied dimers serve as the photoinduced charge carriers, akin to the holons and doublons in the Hubbard model.
Abstract We consider the Hubbard model at half filling, driven by an external, stationary laser field. This stationary, but periodic in time, electromagnetic field couples to the charge current, i.e. it induces an extra contribution to the hopping amplitude in the Hubbard Hamiltonian (photo‐induced hopping). We generalize the dynamical mean‐field theory (DMFT) for nonequilibrium with periodic‐in‐time external fields, using a Floquet mode representation and the Keldysh formalism. We calculate the non‐equilibrium electron distribution function, the density of states and the optical DC conductivity in the presence of the external laser field for laser frequencies above and below the Mott‐Hubbard gap. The results demonstrate that the system exhibits an insulator‐metal transition as the frequency of the external field is increased and exceeds the Mott‐Hubbard gap. This corresponds to photo‐induced excitations into the upper Hubbard band.
We describe the temporal evolution of the time-resolved photoemission response of the spinless Falicov-Kimball model driven out of equilibrium by strong applied fields. The model is one of the few possessing a metal-insulator transition and admitting an exact solution in the time domain. The nonequilibrium dynamics, evaluated using an extension of dynamical mean-field theory, show how the driven system differs from two common viewpoints---a quasiequilibrium system at an elevated effective temperature (the ``hot'' electron model) or a rapid interaction quench (``melting'' of the Mott gap)---due to the rearrangement of electronic states and redistribution of spectral weight. The results demonstrate the inherent trade-off between energy and time resolution accompanying the finite width probe pulses, characteristic of those employed in pump-probe time-domain experiments, which can be used to focus attention on different aspects of the dynamics near the transition.