Floquet perturbation theory: formalism and application to low-frequency limit

Rodriguez-Vega, Martin; Lentz, M.; Seradjeh, Babak

doi:10.1088/1367-2630/aade37

Cited by 64 publications

(29 citation statements)

References 72 publications

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“…Note that for such strong driving, the Floquet bands are shifted somewhat with respect to the equilibrium band, and hence the positions of the gaps are shifted to smaller momenta than in the weak-driving limit. This effect, related to the Bloch-Siegert shift, originates from the low-frequency limit of the Floquet Hamiltonian, where the Floquet bands are given by the average energy of the equilibrium band that electrons experience during one cycle 45 (unlike in the high-frequency limit, where the average Hamiltonian is experienced). This average energy is higher (lower) than the static energy on the upper (lower) branch of the Dirac cone.…”

Section: S6 Substrate Effectsmentioning

confidence: 99%

Light-induced anomalous Hall effect in graphene

et al. 2019

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Many striking non-equilibrium phenomena have been discovered or predicted in opticallydriven quantum solids 1 , ranging from light-induced superconductivity 2,3 to Floquetengineered topological phases 4-8 . These effects are expected to lead to dramatic changes in electrical transport, but can only be comprehensively characterized or functionalized with a direct interface to electrical devices that operate at ultrafast speeds 1-8 . Here, we make use of laser-triggered photoconductive switches 9 to measure the ultrafast transport properties of monolayer graphene, driven by a mid-infrared femtosecond pulse of circularly polarized light. The goal of this experiment is to probe the transport signatures of a predicted light-induced topological band structure in graphene 4,5 , similar to the one originally proposed by Haldane 10 . We report the observation of an anomalous Hall effect in the absence of an applied magnetic field. We also extract quantitative properties of the non-equilibrium state. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect the effective band structure expected from Floquet theory. This includes a ∼60 meV wide conductance plateau centered at the Dirac point, where a gap of approximately equal magnitude is expected to open. We also find that when the Fermi level lies within this plateau, the estimated anomalous Hall conductance saturates around ∼1.8±0.4 e 2 /h.Optical driving has been proposed as a means to engineer topological properties in topologically trivial systems 4-8 . One proposal for such a 'Floquet topological insulator' is based on breaking time-reversal symmetry in graphene through a coherent interaction with circularly polarized light 4 . In this theory, the light field drives electrons in circular trajectories through the band structure (Fig. 1a). Close to the Dirac point, these states are predicted to acquire a non-adiabatic Berry phase every optical cycle, which is equal and opposite for the upper and lower band. This time-averaged extra phase accumulation amounts to an energy * These authors contributed equally to this work

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Section: S6 Substrate Effectsmentioning

confidence: 99%

Light-induced anomalous Hall effect in graphene

et al. 2019

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“…This corresponds to considering only the process whose frequency is closest to the parametric resonance condition. Effects coming from resonant processes are expected to strongly dominate over the nonresonant ones [58,59]. Finally, we note that symmetries impose further constraints on the allowed nonlinear processes.…”

Section: Reflectivity Of Floquet Mediummentioning

confidence: 90%

Parametric resonance of Josephson plasma waves: A theory for optically amplified interlayer superconductivity in YBa2Cu3O6+x

et al. 2020

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Nonlinear interactions between collective modes play a definitive role in far out of equilibrium dynamics of strongly correlated electron systems. Understanding and utilizing these interactions is crucial to photocontrol of quantum many-body states. One of the most surprising examples of strong mode coupling is the interaction between apical oxygen phonons and Josephson plasmons in bilayer YBa 2 Cu 3 O 6+x superconductors. Experiments by Hu et al. [Nat. Mater. 13, 705 (2014)] and Kaiser et al. [Phys. Rev. B 89, 184516 (2014)] showed that below T c , photoexcitation of phonons leads to enhancement and frequency shifts of Josephson plasmon edges, while above T c , photoexcited phonons induce plasmon edges even when there are no discernible features in the equilibrium reflectivity spectrum. Recent experiments by von Hoegen et al. (arXiv:1911.08284) also observed parametric generation of Josephson plasmons from photoexcited phonons both below T c and in the pseudogap phase. In this paper, we present a theoretical model of three-wave phonon-plasmon interaction arising from changes of the in-plane superfluid stiffness caused by the apical oxygen motion. Analysis of the parametric instability of plasmons based on this model gives frequencies of the most unstable plasmons that are in agreement with experimental observations. We also discuss how strong parametric excitation of Josephson plasmons can explain pump-induced changes in the terahertz reflectivity of YBa 2 Cu 3 O 6+x in the superconducting state, including frequency shifts and sharpening of Josephson plasmon edges, as well as appearance of a new peak around 2 THz. An interesting feature of this model is that overdamped Josephson plasmons do not give any discernible features in reflectivity in equilibrium, but can develop plasmon edges when parametrically excited. We suggest that this mechanism explains photoinduced plasmon edges in the pseudogap phase of YBa 2 Cu 3 O 6+x .

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“…can be found for all frequencies (see for instance [102]). Let us discuss how the flow equations apply to this model.…”

Section: Fixed Point Stability and The Properties Of The Exact Flmentioning

confidence: 97%

Flow Equation Approach to Periodically Driven Quantum Systems

et al. 2019

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We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequencyand drive strength-regimes that are usually inaccessible via high frequency ω expansions in the parameter h/ω, where h is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy-model, and test an approximate version of it on both interacting and non-interacting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel non-equilibrium regimes and behaviors in driven quantum many-particle systems.

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Floquet perturbation theory: formalism and application to low-frequency limit

Cited by 64 publications

References 72 publications

Light-induced anomalous Hall effect in graphene

Light-induced anomalous Hall effect in graphene

Parametric resonance of Josephson plasma waves: A theory for optically amplified interlayer superconductivity in YBa2Cu3O6+x

Flow Equation Approach to Periodically Driven Quantum Systems

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