Low-frequency and Moiré–Floquet engineering: A review

Rodriguez-Vega, Martin; Vogl, Michael; Fiete, Gregory A.

doi:10.1016/j.aop.2021.168434

Cited by 60 publications

(41 citation statements)

References 222 publications

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“…Here we will briefly discuss its salient features, chart out the basic computations involved, and discuss its recent application to integrable periodically driven systems. A more detailed discussion of possible approaches to Floquet systems at low drive frequencies is given in reference [69].…”

Section: Adiabatic-impulse Approximationmentioning

confidence: 99%

Analytic approaches to periodically driven closed quantum systems: methods and applications

Sen¹,

Sen²,

Sengupta³

2021

J. Phys.: Condens. Matter

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We present a brief overview of some of the analytic perturbative techniques for the computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many-body system. The key technical points about each of the methods discussed are presented in a pedagogical manner. They are followed by a brief account of some chosen phenomena where these methods have provided useful insights. We provide an extensive discussion of the Floquet-Magnus (FM) expansion, the adiabatic-impulse approximation, and the Floquet perturbation theory. This is followed by a relatively short discourse on the rotating wave approximation, a FM resummation technique and the Hamiltonian flow method. We also provide a discussion of some open problems which may possibly be addressed using these methods.

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Section: Adiabatic-impulse Approximationmentioning

confidence: 99%

Analytic approaches to periodically driven closed quantum systems: methods and applications

Sen¹,

Sen²,

Sengupta³

2021

J. Phys.: Condens. Matter

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“…The possibility of inducing a nontrivial topology in condensed matter systems by means of an electromagnetic drive has been the subject of many research works in recent years [1][2][3][4][5][6][7][8][9][10], some of which have focused in Dirac systems such as graphene [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Dirac materials under linear polarized light: quantum wave function time evolution and topological Berry phases as classical charged particles trajectories under electromagnetic fields

et al. 2022

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The response of electrons under linearly polarized light in Dirac materials as borophene or graphene is analyzed in a continuous wave regime for an arbitrary intense field. Using a rotation and a time-dependent phase transformation, the wave function evolution is shown to be governed by a spinor-component decoupled Whittaker-Hill equation. The numerical solution of these equations enables to find the quasienergy spectrum. For borophene it reveals a strong anisotropic response. By applying an extra unitary transformation, the wave functions are proven to follow an Ince equation. The evolution of the real and imaginary parts of the wave function is interpreted as the trajectory of a classical charged particle under oscillating electric and magnetic field. The topological properties of this forced quantum system are studied using this analogy. In particular, in the adiabatic driving regime, the system is described with an effective Matthieu equation while in the non-adiabatic regime the full Whittaker-Hill equation is needed. From there, it is possible to separate the dynamical and Berry phase contributions to obtain the topological phase diagram due to the driving. Therefore, a different path to perturbation theory is developed to obtain time-driven topological phases.

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“…The quenching of the kinetic energy of flatband electrons might allow one to reach the regime of strong LMC more easily than in strongly dispersive materials [40]. Specifically for TBG and other moiré systems, there have been first theoretical explorations of Floquet engineering [129][130][131][132][133][134][135][136][137] and nonlinear optical responses [138]. Recently a measured strong mid-infrared photoresponse in bilayer graphene at small twist angles was reported [139].…”

Section: Introductionmentioning

confidence: 99%

Light-matter coupling and quantum geometry in moiré materials

et al. 2021

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Quantum geometry has been identified as an important ingredient for the physics of quantum materials and especially of flat-band systems, such as moiré materials. On the other hand, the coupling between light and matter is of key importance across disciplines and especially for Floquet and cavity engineering of solids. Here we present fundamental relations between light-matter coupling and quantum geometry of Bloch wave functions, with a particular focus on flat-band and moiré materials, in which the quenching of the electronic kinetic energy could allow one to reach the limit of strong light-matter coupling more easily than in highly dispersive systems. We show that, despite the fact that flat bands have vanishing band velocities and curvatures, light couples to them via geometric contributions. Specifically, the intraband quantum metric allows diamagnetic coupling inside a flat band; the interband Berry connection governs dipole matrix elements between flat and dispersive bands. We illustrate these effects in two representative model systems: (i) a sawtooth quantum chain with a single flat band and (ii) a tight-binding model for twisted bilayer graphene. For (i) we highlight the importance of quantum geometry by demonstrating a nonvanishing diamagnetic light-matter coupling inside the flat band. For (ii) we explore the twist-angle dependence of various light-matter coupling matrix elements. Furthermore, at the magic angle corresponding to almost flat bands, we show a Floquet-topological gap opening under irradiation with circularly polarized light despite the nearly vanishing Fermi velocity. We discuss how these findings provide fundamental design principles and tools for light-matter-coupling-based control of emergent electronic properties in flat-band and moiré materials.

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Low-frequency and Moiré–Floquet engineering: A review

Cited by 60 publications

References 222 publications

Analytic approaches to periodically driven closed quantum systems: methods and applications

Analytic approaches to periodically driven closed quantum systems: methods and applications

Dirac materials under linear polarized light: quantum wave function time evolution and topological Berry phases as classical charged particles trajectories under electromagnetic fields

Light-matter coupling and quantum geometry in moiré materials

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