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arXiv:1610.02613 · Physica Scripta

Theoretical description of pump/probe experiments in electron-mediated charge-density-wave insulators

James K. Freericks, O. P. Matveev, Wen Shen, Andrij M. Shvaika, Thomas Devereaux

Published Feb 13, 2017• 16 citations
arXivHTMLPDF

Abstract

Abstract In this review, we develop the formalism employed to describe charge-density-wave insulators in pump/probe experiments that use ultrashort driving pulses of light. The theory emphasizes exact results in the simplest model for a charge-density-wave insulator (given by a noninteracting system with two bands and a gap) and employs nonequilibrium dynamical mean-field theory to solve the Falicov–Kimball model in its ordered phase. We show how to develop the formalism and how the solutions behave. Care is taken to describe the details behind these calculations and to show how to verify their accuracy via sum-rule constraints.

DOI
10.1088/1402-4896/aa5b6c

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Abstract In this review, we develop the formalism employed to describe charge-density-wave insulators in pump/probe experiments that use ultrashort driving pulses of light. The theory emphasizes exact results in the simplest model for a charge-density-wave insulator (given by a noninteracting system with two bands and a gap) and employs nonequilibrium dynamical mean-field theory to solve the Falicov–Kimball model in its ordered phase. We show how to develop the formalism and how the solutions behave. Care is taken to describe the details behind these calculations and to show how to verify their accuracy via sum-rule constraints.
We present a theoretical description of time-resolved photoemission in charge-density-wave insulators that derive their ordering from electron nesting effects. In these pump/probe experiments, a large amplitude (but short duration) pump pulse excites the system into nonequilibrium and then a higher frequency low amplitude probe pulse photoexcites electrons, which are measured at the detector. We describe effects of electron correlations on the photoelectron spectroscopy and provide details for the theoretical techniques used to solve these problems. We also show how the gap fills in as the system is excited, even though the order parameter does not go to zero. The theory is developed for the Falicov-Kimball model, which can be solved exactly with nonequilibrium dynamical mean-field theory.
We determine the exact time-resolved photoemission spectroscopy for a nesting driven charge density wave (described by the spinless Falicov-Kimball model within dynamical mean-field theory). The pump-probe experiment involves two light pulses: the first is an ultrashort intense pump pulse that excites the system into nonequilibrium, and the second is a lower amplitude, higher frequency probe pulse that photoexcites electrons. We examine three different cases: the strongly correlated metal, the quantum-critical charge density wave, and the critical Mott insulator. Our results show that the quantum critical charge density wave has an ultraefficient relaxation channel that allows electrons to be de-excited during the pump pulse, resulting in little net excitation. In contrast, the metal and the Mott insulator show excitations that are closer to what one expects from these systems. In addition, the pump field produces spectral band narrowing, peak sharpening, and a spectral gap reduction, all of which rapidly return to their field free values after the pump is over.
Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical mean-field theory to exactly solve for the nonlinear response of an electron-mediated charge-density-wave-ordered material. We examine both the dc current and the order parameter of the conduction electrons as the ordered system is driven by the electric field. Although the formalism we develop applies to all models, for concreteness, we examine the charge-density-wave phase of the Falicov-Kimball model, which displays a number of anomalous behaviors including the appearance of subgap density of states as the temperature increases. These subgap states should have a significant impact on transport properties, particularly the nonlinear response of the system to a large dc electric field.
We develop the theory for nonresonant Raman scattering of strongly correlated electrons in time-resolved pump- probe experiments. The electrons are initially pumped with an intense pulse of light and then a probe pulse measures the Raman response function after an adjustable time delay. We describe how the width of the probe pulse and the strength of the electron correlations affect the Raman cross section. The theory is developed for the case of B1g symmetry, where incident and scattered light are polarized perpendicular to each other. We illustrate the exact solution with the Falicov-Kimball model, which is solved via nonequilibrium dynamical mean-field theory.
We derive the dynamical mean-field theory equations for transport in an ordered charge-density-wave phase on a bipartite lattice. The formalism is applied to the spinless Falicov-Kimball model on a hypercubic lattice at half filling. We determine the many-body density of states, the dc charge and heat conductivities, and the optical conductivity. Vertex corrections continue to vanish within the ordered phase, but the density of states and the transport coefficients show anomalous behavior due to the rapid development of thermally activated subgap states. We also examine the optical sum rule and sum rules for the first three moments of the Green's functions within the ordered phase and see that the total optical spectral weight in the ordered phase either decreases or increases depending on the strength of the interactions.
Abstract Modern time-resolved spectroscopy experiments on quantum materials raise the question, how strong electron-electron interactions, in combination with periodic driving, form unconventional transient states. Here we show using numerically exact methods that in a driven strongly interacting charge-density-wave insulator a band-like resonance in the gap region is formed. We associate this feature to the so-called Villain mode in quantum-magnetic materials, which originates in moving domain walls induced by the interaction. We do not obtain the in-gap band when driving a non-interacting charge density wave model. In contrast, it appears in the interacting system also in equilibrium at intermediate temperatures and in the short-time evolution of the system after a quantum quench to the lowest-order high-frequency effective Floquet Hamiltonian. Our findings connect the phenomenology of a periodically driven strongly correlated system and its quench dynamics to the finite-temperature dynamical response of quantum-magnetic materials and will be insightful for future investigations of strongly correlated materials in pump-probe setups.