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

B. Moritz, A. F. Kemper, M. Sentef, T. P. Devereaux, and J. K. Freericks

Phys. Rev. Lett. 111, 077401 – Published 12 August 2013

Abstract

We examine electron-electron mediated relaxation following ultrafast electric field pump excitation of the fermionic degrees of freedom in the Falicov-Kimball model for correlated electrons. The results reveal a dichotomy in the temporal evolution of the system as one tunes through the Mott metal-to-insulator transition: in the metallic regime relaxation can be characterized by evolution toward a steady state 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 complicated electronic distribution as a function of momentum. We characterize the behavior by studying changes in the energy, photoemission response, and electronic distribution as functions of time. This relaxation may be observable qualitatively on short enough time scales that the electrons behave like an isolated system not in contact with additional degrees of freedom which would act as a thermal bath, especially when using strong driving fields and studying materials whose physics may manifest the effects of correlations.

Received 4 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.111.077401

Authors & Affiliations

B. Moritz^1,2,3,*, A. F. Kemper¹, M. Sentef¹, T. P. Devereaux¹, and J. K. Freericks⁴

¹Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
²Department of Physics and Astrophysics, University of North Dakota, Grand Forks, North Dakota 58202, USA
³Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
⁴Department of Physics, Georgetown University, Washington, DC 20057, USA

^*moritz.physics@gmail.com

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Vol. 111, Iss. 7 — 16 August 2013

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Images

Figure 1
(a) The electric field pump pulse that leads to the temporal evolution shown in panels (b) and (c) has a maximum intensity $E_{\max } = 24 E_{0}$ (normalized in the panel), modulation frequency $ω_{p} = 0.5 t^{*}$ , and characteristic width $σ_{p} = 5 / t^{*}$ . (b),(c) Time-resolved pump-probe photoemission response for (b) metallic $U = 0.5 t^{*}$ ) and (c) insulating $U = 2 t^{*}$ ) systems determined for a probe pulse with characteristic width $σ_{b} = 2 / t^{*}$ . See the Supplemental Material [39] for a discussion of the evaluation of the photoemission cross section and the definition of the Gaussian probe pulse.Reuse & Permissions
Figure 2
Instantaneous power delivered to (a) metallic ( $U = 0.5 t^{*}$ ) and (b) insulating ( $U = 2 t^{*}$ ) systems discussed in Fig. 1. (c),(d) As a closed system, the change in total energy may be determined by integrating the instantaneous power [upper oscillating, black 2c or red 2d curves] or by direct calculation from the time derivative of the local propagator (lower oscillating, green curves). The constant offset (relatively flat, bottom, blue lines) represents the initial, equilibrium value in each case. The insets highlight times near the center of the pump pulse between $- 2.5 / t^{*}$ and $2.5 / t^{*}$ that show rapid variation in each quantity.Reuse & Permissions
Figure 3
Quasithermal fits of the steady-state photoemission response (characteristic probe width $σ_{b} = 2 / t^{*}$ ) for (a) metallic ( $U = 0.5 t^{*}$ ) and (b) insulating ( $U = 2 t^{*}$ ) systems, respectively, with the effective temperature shown in parenthesis. The fits (solid black) are determined by extracting the temperature from the total energy, while the best-fit quasithermal response (dashed red) has been determined by the least-squares method (LSQ).Reuse & Permissions
Figure 4
(a)–(d) A simple cartoon depicting the influence of an applied electric field on a noninteracting one-dimensional band metal at half-filling. (a),(c) The band energy ( $ε_{k}$ , red highlight) and normalized band velocity ( $v_{k}$ , blue highlight) distributions in equilibrium and under the influence of an applied electric field, respectively. In one dimension each band energy is associated with two band velocities [right ( $+$ ) and left ( $-$ )]. In higher dimensions a distribution of velocities is associated with each band energy. (b),(d) The equivalent distribution shown in a two-dimensional band energy-velocity space with the axes labels annotated in each panel. The gray shading is a guide to the eye. (e),(f) Equal-time band energy-velocity distribution functions for the metallic ( $U = 0.5 t^{*}$ ) and insulating ( $U = 2 t^{*}$ ) regimes of Figs. 1b, 1c, respectively, for various times (units of $1 / t^{*}$ ). The band energy-velocity space spans a radius of $3.9 t^{*}$ with the center of each plot at the origin ( $0 t^{*}$ , $0 t^{*}$ ) as indicated by the band energy-velocity axes in the top panels. A time-lapse sequence of images for both cases with finer resolution can be found in the Supplemental Material [39].Reuse & Permissions

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