Floquet engineering of twisted double bilayer graphene

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

doi:10.1103/physrevresearch.2.033494

Cited by 42 publications

(22 citation statements)

References 91 publications

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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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Section: Introductionmentioning

confidence: 99%

Light-matter coupling and quantum geometry in moiré materials

et al. 2021

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“…The quenching of the kinetic energy of flat-band 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

Topp,

Eckhardt,

Kennes

et al. 2021

Preprint

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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 intra-band quantum metric allows diamagnetic coupling inside a flat band; the inter-band 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 twistangle 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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“…In this context various techniques have been developed to achieve a time-independent description [45][46][47][48][49][50][51][52][53][54][55][56][57]. More recently, the moiré and Floquet approaches have been combined to make theoretical predictions about various topological phases in moiré materials [39,[58][59][60][61][62].…”

Section: Introductionmentioning

confidence: 99%

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

Benlakhouy,

Jellal,

Bahlouli

et al. 2021

Preprint

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We study the magnetic field induced Hofstadter butterfly in twisted bilayer graphene (TBG) in various kinds of situations. First, we study the equilibrium case and identify the interlayer hopping processes that are most crucial for the appearance of a Hofstadter butterfly. Surprisingly, the hopping processes that are important for the appearance of the Hofstadter butterfly can be categorized as AA stacking type -that is interlayer hoppings between equivalent sublattices. This is in contrast to AB/BA-type hoppings that are important for the appearance of flat bands in magic angle TBG and were discussed in [1]. We also find that if AB-type interlayer-hopping processes are turned off the resulting model is chiral but differs from the model discussed in [1]. Therefore, TBG has two separate chiral limits -one of them is important to understand the formation of flat bands and the other for the Hofstadter butterfly. Taking this as motivation we discuss how the role of AA-type hoppings in combination with lattice relaxation effects can make individual Landau levels slightly harder to resolve in an experimental setting than one would expect from a non-relaxed lattice setting. Finally, we consider the impact of different forms of light on the fractal structure of the butterfly. Particularly, we study the impact of circularly polarized light and longitudinal light originating from a waveguide. As the system is exposed to circularly polarized light we find butterflies with increasingly pronounced asymmetry with respect to energy E = 0. This is due to the introduction of a gap term that breaks the chiral symmetries for both of the two chiral limits mentioned above. Lastly, we study the effect of longitudinal light that can be produced at the exit of a waveguide. Here, we find that no additional terms that break chiral symmetry are introduced. Therefore, it is found to lead to no increase in asymmetry of the energy spectrum. In fact, we identify specific experimentally accessible driving regimes in which the TBG achieves any of the two chiral limits.

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Floquet engineering of twisted double bilayer graphene

Cited by 42 publications

References 91 publications

Light-matter coupling and quantum geometry in moiré materials

Light-matter coupling and quantum geometry in moiré materials

Light-matter coupling and quantum geometry in moiré materials

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

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