Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths

Abstract

External driving is emerging as a promising tool for exploring new phases in quantum systems. The intrinsically nonequilibrium states that result, however, are challenging to describe and control. We study the steady states of a periodically driven one-dimensional electronic system, including the effects of radiative recombination, electron-phonon interactions, and the coupling to an external fermionic reservoir. Using a kinetic equation for the populations of the Floquet eigenstates, we show that the steady-state distribution can be controlled using the momentum and energy relaxation pathways provided by the coupling to phonon and Fermi reservoirs. In order to utilize the latter, we propose to couple the system and reservoir via an energy filter which suppresses photon-assisted tunneling. Importantly, coupling to these reservoirs yields a steady state resembling a band insulator in the Floquet basis. The system exhibits incompressible behavior, while hosting a small density of excitations. We discuss transport signatures and describe the regimes where insulating behavior is obtained. Our results give promise for realizing Floquet topological insulators.

Towards properties on demand in quantum materials

“…Under periodic electromagnetic excitation with frequency Ω (panel c), electronic bands become dressed, which manifests itself as a 'Floquet' copy of the original band shifted in energy by hΩ [61][62][63][64][65] . Even though the driving field oscillates at frequency Ω, crystals effectively rectify these oscillations, yielding a quasi-static dispersion on the timescale of the excitation pulse 65,78 .…”

“…In addition, questions about how to control the steady-state occupation of Floquet bands and to mitigate heating effects remain outstanding. However, recent advancements in ultrafast experimental techniques, theoretical simulations of time-domain experiments 61,62 and the development of driving protocols for population and thermal management 63,64 are boldly moving this field forward 65 . The recent successful imaging of a Floquet band structure (Fig.…”

Floquet-Boltzmann equation for periodically driven Fermi systems

“…A similar semiclassical kinetic equation was also derived in a recent preprint of Seetharam et al [27]. In contrast to our work, they considered electron-phonon coupling instead of fermion-fermion interactions.…”

“…For a generic closed system, one can expect that in the longtime limit, t → ∞, the system approaches the state with the highest entropy consistent with the conservation laws. In the absence of some cooling mechanism, e.g., by an external bath [27] or by emitting radiation, one can therefore expect that generic interacting Floquet systems heat up to infinite temperatures [28] (an exception are many-body localized systems [29]). This important (and well-known) aspect has received relatively little attention in previous studies.…”

“…Technically, Ref. [27] used an equation-of-motion approach. While this approach is, perhaps, less well suited to investigate limitations of semiclassics, we expect that in the semiclassical limit it gives results equivalent to our derivation.…”