Quantum Hall effect in ac driven graphene: From the half-integer to the integer case

Ding, Kai-He; Lim, Lih-King; Su, Gang; Weng, Zheng-Yu

doi:10.1103/physrevb.97.035123

Cited by 21 publications

(15 citation statements)

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“…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. Specifically, previous works have focused on the kicked-Harper model [4,[74][75][76].…”

Section: Introductionmentioning

confidence: 82%

“…Other cases include MLG subjected to a uniform perpendicular magnetic field B in combination with a laser. Here, the Floquet Hofstadter butterfly exhibits a richer structure than the equilibrium case [79][80][81]. We hope to find a similarly light induced richer structure and therefore, we will try to fill this gap and study the Hofstadter butterfly in TBLG under the influence of different forms of light.…”

Section: Introductionmentioning

confidence: 99%

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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: 82%

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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“…Due to its unique properties, such as the unusual half-integer quantum Hall effect [1,2] and mass-less Dirac fermion behavior [3,4], graphene has many potential applications in the fields of novel physics, chemistry, optics, and mechanics [5,6], and as realistic technology transfer in the fields of membrane technology [7], energy [8], photodetection [9], and plasmonics [10]. Since the successful preparation of the first stable graphene flake at room temperature by peeling highly oriented pyrolytic graphite (HOPG) [11], people have developed many methods to prepare graphene, including monolayer [12,13], bilayer [14,15], and few-layer graphene [16,17], in the form of powder [18], flake [19], and film [20].…”

Section: Introductionmentioning

confidence: 99%

Growth of Ordered Graphene Ribbons by Sublimation Epitaxy

et al. 2018

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Ordered graphene ribbons were grown on the surface of 4° off-axis 4H-SiC wafers by sublimation epitaxy, and characterized by using scanning electron microscopy (SEM), atomic force microscopy (AFM) and micro-Raman spectroscopy (μ-Raman). SEM showed that there were gray and dark ribbons on the substrate surface, and AFM further revealed that these ordered graphene ribbons had clear stepped morphologies due to surface step-bunching. It was shown by μ-Raman that the numbers of graphene layers of these two types of regions were different. The gray region was composed of mono- or bilayer ordered graphene ribbon, while the dark region was of tri- or few-layer ribbon. Meanwhile, ribbons were all homogeneous and had a width up to 40 μm and a length up to 1000 μm, without micro defects such as grain boundaries, ridges, or mono- and few-layer graphene mixtures. The results of this study are useful for optimized growth of high-quality graphene film on silicon carbide crystal.

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“…In addition, the Hofstadter butterfly has been proposed in nanophotonic devices [132], and for bosons in optical lattices [133][134][135], where it has also been experimentally realized [136,137]. All these studies were done in equilibrium, and so far out-of-equilibrium Hofstadter setups have not received much attention, although driven systems have been under intense scrutiny recently [138][139][140][141][142][143][144][145][146][147][148][149][150][151][152][153]. In particular, time-periodic driving attracted great interest because it can be conveniently described in the framework of Floquet theory [138,140,154,155].…”

Section: Discussionmentioning

confidence: 99%

“…In Ref. [153], a transition from the half-integer to the integer quantum Hall effect has been theoretically proposed to occur upon elliptical driving of an ac field.…”

Section: Discussionmentioning

confidence: 99%

Crystalline topological phases

Kooi¹

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under the supervision of prof. dr. Cristiane de Morais Smith and prof. Carmine Ortix.In Chapter 1, a brief introduction to some key concepts that will appear throughout this thesis as well as an outline for the rest of the thesis are given. Chapters 2-5 contain original research based on the articles found in the list of publications. Chapter 6 contains the conclusions, after which a Dutch summary, a brief CV and the bibliography can be found. I wish the reader much enjoyment reading this thesis.

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Quantum Hall effect in ac driven graphene: From the half-integer to the integer case

Cited by 21 publications

References 50 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

Growth of Ordered Graphene Ribbons by Sublimation Epitaxy

Crystalline topological phases

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