Electron-Mediated Relaxation Following Ultrafast Pumping of Strongly Correlated Materials: Model Evidence of a Correlation-Tuned Crossover between Thermal and Nonthermal States

Abstract

We examine electron-electron mediated relaxation following excitation of a correlated system by an ultrafast electric field pump pulse. The results reveal a dichotomy in the temporal evolution as one tunes through a Mott metal-to-insulator transition: in the metallic regime relaxation can be characterized by evolution toward a steady-state electronic distribution well described by Fermi-Dirac statistics with an increased effective temperature; however, in the insulating regime this quasithermal paradigm breaks down with relaxation toward a nonthermal state with a more complicated electronic distribution that does not vary monotonically as a function of energy. We characterize the behavior by studying changes in the energy, photoemission response, and electronic distribution as functions of time. Qualitatively these results should be observable on short enough time scales that the electrons behave like an isolated system not in contact with additional degrees of freedom which can act as a thermal bath. Importantly, proper modeling used to analyze experimental findings should account for this behavior, especially when using strong driving fields or studying materials whose physics may manifest the effects of strong correlations. -6, 8-10, 12-18] On sufficiently short time scales, the initial recovery in these systems following an ultrafast pump pulse should be dominated by electron-electron scattering which on its own can drive the system into a new steady-state. Conventional analysis has been based on a quasithermal paradigm ("hot electron" or multi-temperature models); [19,20] however, there have been few tests of the validity of its underlying assumptions as a function of the strength of electronic correlations, [21] in particular as one tunes between the two regimes of a metal-to-insulator transition (MIT). [22] The MIT driven by electronic correlations usually is accompanied by a number of interesting ordering phenomena among the spin, charge, and orbital degrees of freedom in a material. An understanding of the key physics which leads to these emergent phases is often at the heart of pump-probe experiments in condensed matter systems, including high-T c cuprate superconductors, [23] nickelates, manganites, ruthenates, vanadates, [22] and even organic materials. [24][25][26] A number of experimental parameters can be used to tune across the MIT including doping and chemical substitution, pressure, and applied fields. What can be learned about the underlying physics leading to these phases as a function of these key parameters requires an understanding of the proper paradigm in which to ask the relevant questions and conduct analysis of experimental data. This is in addition to what can be learned by tuning the interaction parameters of model systems simulated in fermionic or bosonic cold atom mixtures and performing the experimental equivalent of time-resolved, pump-probe measurements. [27][28][29] In this Letter we discuss the evolution of an electronic system described in equilibrium by a simple Hamiltoni...

Thermalization of field driven quantum systems

“…The classification of different scenarios is simplified and clarified by examining the behavior in the time domain rather than the more commonly studied frequency domain. It is interesting to also study field driven systems in other contexts, like in the response to a pulse, where the final state can possibly thermalize at any temperature since the final Hamiltonian is the same as the initial Hamiltonian the system had in equilibrium, and in the long time limit no current flows1920.…”

“…The Green's functions can be employed to calculate the kinetic energy, potential energy, and current in the presence of a driving field20. The bandstructure satisfies in the limit of d approaching infinity, with A(t) the component of the vector potential, which is nonzero only for positive times.…”

Phonon-enhanced relaxation and excitation in the Holstein-Hubbard model

“…The twotemperature model, 18 which assumes that the electronic relaxation is fast compared to the time scale of phonons, is certainly inadequate in this case, since it has been demonstrated that the relaxation time in purely electronic systems with a gap can be much longer than typical phonon oscillation times. 19,20 It is therefore important to develop a formalism which can describe the feedback of the quantum phonons on the electronic relaxation process and the effect of the nonequilibrium state of the electrons on the evolution of the phonons.…”

Ultra-fast photo-carrier relaxation in Mott insulators with short-range spin correlations

“…However, while DMFT has been used extensively to study the antiferromagnetic phase with long-range order 22 23 26 27 28 , it neglects short-range spin-correlations in the paramagnetic phase. Relaxation processes in DMFT are thus restricted to electron-electron scattering, leading to a very slow or absent redistribution of spectral weight 29 30 31 , which may correctly describe systems at high temperature and high fluence, in which spin-correlations have been melted away (see below). To overcome these limitations, we go beyond DMFT and implement a nonequilibrium version of the dynamical-cluster approximation (DCA) 32 , which maps a lattice problem to a small cluster embedded in a self-consistent bath, and thus allows us to incorporate the effect of short-range correlations on the real-time evolution of an extended lattice system.…”