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arXiv:1811.03386 · Physical review. B./Physical review. B

Nonequilibrium susceptibility in photoinduced Floquet states

Atsushi Ono, Sumio Ishihara

Published Aug 13, 2019• 13 citations
arXivHTMLPDF

Abstract

Nonequilibrium susceptibility in photoinduced Floquet states is studied. We analyze an electron system coupled with a heat bath in a time-periodic electric field. Spin/charge susceptibility is formulated on the basis of the Floquet Green's function method, and is calculated numerically in a wide range of amplitude and frequency of light. When the frequency is larger than the bandwidth, the susceptibility is enhanced due to the dynamical localization effect, and their peak positions in the momentum space are shifted by the Fermi surface deformation. In the case of the small frequency and amplitude, a multiple-peak structure emerges in the susceptibility, originating from the multiple Floquet bands which cross the Fermi level of the bath. To confirm those numerical results and provide the interpretation, a perturbative expression of the susceptibility is derived for small electric-field amplitude.

DOI
10.1103/physrevb.100.075127

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Nonequilibrium susceptibility in photoinduced Floquet states is studied. We analyze an electron system coupled with a heat bath in a time-periodic electric field. Spin/charge susceptibility is formulated on the basis of the Floquet Green's function method, and is calculated numerically in a wide range of amplitude and frequency of light. When the frequency is larger than the bandwidth, the susceptibility is enhanced due to the dynamical localization effect, and their peak positions in the momentum space are shifted by the Fermi surface deformation. In the case of the small frequency and amplitude, a multiple-peak structure emerges in the susceptibility, originating from the multiple Floquet bands which cross the Fermi level of the bath. To confirm those numerical results and provide the interpretation, a perturbative expression of the susceptibility is derived for small electric-field amplitude.
We present a framework to determine nonequilibrium steady states in strongly correlated electron systems in the presence of dissipation. This is demonstrated for a correlated electron (Falicov-Kimball) model attached to a heat bath and irradiated by an intense pump light, for which an exact solution is obtained with the Floquet method combined with the nonequilibrium dynamical mean-field theory. On top of a Drude-like peak indicative of photometallization as observed in recent pump-probe experiments, new nonequilibrium phenomena are predicted to emerge, where the optical conductivity exhibits dip and kink structures around the frequency of the pump light, a midgap absorption arising from photoinduced Floquet subbands, and a negative attenuation (gain) due to a population inversion.
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.
The interaction of time-dependent electromagnetic fields with electrons in quantum materials can give rise to many both fundamentally interesting as well as technologically relevant phenomena like transient band structure manipulations or the emergence of prethermal states of matter, which are not a result of heating. This thesis contributes theoretical insights to both these topics: We model the interference of Floquet and Volkov side bands, which are a result of the dressing of electron states by light, in a time-resolved angle-resolved photoemission spectroscopy (ARPES) experiment. Furthermore, we analyze the emergence of a band-like feature in the non-equilibrium spectral function of a one-dimensional charge-density wave insulator upon periodic driving. Secondly, we use the fermionic truncated Wigner approximation (fTWA), a phase space method for the time evolution of interacting fermions, to study the light-induced order parameter dynamics in SU(N)-symmetric fermionic lattice models. By comparison with exact analytical results for an interaction quench in the Hubbard model, we find that dephasing-induced prethermalization is correctly described by fTWA. We discuss photoinduced prethermal transitions between competing phases of matter in the large-N Hubbard-Heisenberg model and find a pronounced frequency-dependence of the transition. This work contributes to a better understanding of photoinduced order parameter dynamics from a microscopic perspective.
We develop the Floquet-Bloch theory of noninteracting fermions on a periodic lattice in the presence of a constant electric field. As long as the field lies along a reciprocal-lattice vector, time periodicity of the Bloch Hamiltonian is inherited from the evolution of momentum in the Brillouin zone. The corresponding Floquet quasienergies yield the Wannier-Stark ladder with interband couplings included to all orders. These results are compared to perturbative results where the lowest-order interband correction gives the field-induced polarization shift in terms of the electric susceptibility. Additionally, we investigate electronic transport by coupling the system to a bath within the Floquet-Keldysh formalism. We then study the breakdown of the band-projected theory from the onset of interband contributions and Landau-Zener resonances in the band-resolved currents. In particular, we consider the transverse quantum-geometric response in two spatial dimensions due to the Berry curvature. In the strong-field regime, the semiclassical theory predicts a plateau of the geometric response as a function of field strength. Here, we scrutinize the conditions under which the semiclassical results continue to hold in the quantum theory.
By using the Floquet eigenstates, we derive a formula to calculate the high-order harmonic components of the electric current (HHC) in the setup where a monochromatic laser field is turned on at some time. On the basis of this formulation, we study the HHC spectrum of electrons on a one-dimensional chain with a staggered potential to study the effect of multiple sites in the unit cell such as the systems with charge density wave order. With the help of the solution for the Floquet eigenstates, we analytically show that two plateaus of different origins emerge in the HHC spectrum. The widths of these plateaus are both proportional to the field amplitude, but inversely proportional to the laser frequency and its square, respectively. We also show numerically that multistep plateaus appear when both the field amplitude and the staggered potential are strong.