Floquet Hofstadter butterfly on the kagome and triangular lattices

Du, Liang; Chen, Qi; Barr, Aaron; Barr, Ariel Rebekah; Fiete, Gregory A.

doi:10.1103/physrevb.98.245145

Cited by 25 publications

(12 citation statements)

References 54 publications

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“…In particular, we consider the so-called Hofstadter butterfly phenomenon [64], where electrons under the influence of a magnetic field exhibit an energy spectrum that displays fractal patterns. These types of fractal butterfly spectra have been observed experimentally in monolayer graphene (MLG) [65,66], in AB-BLG, placed on a hexagonal boron nitride (hBN) substrate [67], also on square, honeycomb and triangular lattices [68,69], kagome lattices [70] and in TBLG [71][72][73]. While the effect of a periodic drive -in our case light -on the Hofstadter butterfly has been studied in various systems [4,[74][75][76][77][78][79][80][81] it has, to our knowledge, not been studied in the case of TBLG.…”

Section: Introductionmentioning

confidence: 80%

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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Section: Introductionmentioning

confidence: 80%

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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“…For example, topological Edge States (ESs) can occur when a charged particle in a crystal interacts with an external magnetic field [6,7]. The physics of charged particles in a two-dimensional crystalline lattice with an applied strong magnetic field is a well-studied problem for both the single-particle [8][9][10][11][12][13][14] and many-body [15][16][17][18] regimes. There have also been numerous experimental realisations and proposals [7,[19][20][21][22].…”

Section: Introduction a Motivationmentioning

confidence: 99%

Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity

Johnstone,

Colbrook,

Nielsen

et al. 2021

Preprint

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Robust edge transport can occur when charged particles in crystalline lattices interact with an applied external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge states. When the confining lattice geometry is altered to be quasicrystaline, i.e. quasiperiodic, then Bloch's theorem breaks down. However, for the quasicrystalline system, we still expect to observe the basic characteristics of bulk states and current carrying edge states. Here, we show that for quasicrystals in magnetic fields, there is also a third option; the bulk localised transport states. These states share the in-gap nature of the well-known edge states and can support transport along them, but they are fully contained within the bulk of the system, with no support along the edge. This results in transport being possible both along the edge and within distinct regions of the bulk. We consider both finite-size and infinite-size systems, using rigorous error controlled computational techniques that are not prone to finite-size effects. The bulk localised transport states are preserved for infinite-size systems, in stark contrast to the normal edge states. This allows for transport to be observed in infinite-size systems, without any perturbations, defects, or boundaries being introduced. We confirm the ingap topological nature of the bulk localised transport states for finite and infinite-size systems by computing common topological measures; namely the Bott index and local Chern marker. The bulk localised transport states form due to a magnetic aperiodicity arising from the interplay of length scales between the magnetic field and quasiperiodic lattice. Bulk localised transport could have interesting applications similar to those of the edge states on the boundary, but that could now take advantage of the larger bulk of the lattice. The infinite size techniques introduced here, especially the calculation of topological measures, could also be widely applied to other crystalline, quasicrystalline, and disordered models.

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“…Using a combination of spin wave theory and quantum field theory, a magnonic Floquet Hofstadter butterfly is realized in the twodimensional (2D) insulating honeycomb ferromagnet 34 . By considering different Bravais lattice, the driven Hofstadter in Kagome and triangular lattice are studied systematically 35 .…”

Section: Introductionmentioning

confidence: 99%

Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian

Zhao,

Chen,

Tian

et al. 2020

Preprint

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Floquet Hofstadter butterfly on the kagome and triangular lattices

Cited by 25 publications

References 54 publications

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

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

Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity

Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian

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