Moiré edge states in twisted bilayer graphene and their topological relation to quantum pumping

Fujimoto, Manato; Koshino, Mikito

doi:10.1103/physrevb.103.155410

Cited by 19 publications

(10 citation statements)

References 69 publications

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“…To describe quantitatively the TBG band dispersion it is necessary to take into account hopping elements between an increasing number of neighbors due to the rather extended character of the Wannier orbitals representing the flat bands. This model has been intensively used [44][45][46][47] due to its simplicity but, although it exhibits naturally particle/hole symmetry, due to the Wannier obstruction it lacks the characteristic symmetries of the system [35] and leads to moiré minivalleys with vanishing net chirality.…”

Section: A 2b1v Modelmentioning

confidence: 99%

Transport and spectral properties of magic-angle twisted bilayer graphene junctions based on local orbital models

Alvarado

Yeyati

2021

Phys. Rev. B

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Section: A 2b1v Modelmentioning

confidence: 99%

Transport and spectral properties of magic-angle twisted bilayer graphene junctions based on local orbital models

Alvarado

Yeyati

2021

Phys. Rev. B

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“…In this subsection, we compare the present formalism with various approaches to characterize topological pumping adopted in the previous studies [31,[36][37][38][39].…”

Section: E Difference From Other Characterizationsmentioning

confidence: 99%

Topological charge pumping in quasiperiodic systems characterized by Bott index

Yoshii,

Kitamura,

Morimoto

2021

Preprint

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We study topological charge pumping in one-dimensional quasiperiodic systems. Since these systems lack periodicity, we cannot use the conventional approach based on the topological Chern number defined in the momentum space. Here, we develop a general formalism based on a real space picture using the so-called Bott index. We extend the Bott index that was previously used to characterize quantum Hall effects in quasiperiodic systems, and apply it to topological charge pumping in quasiperiodic systems. The Bott index allows us to systematically compute topological indices of charge pumping, regardless of the detail of quasiperiodic models. We apply this formalism to the Fibonacci-Rice-Mele model which we made from Fibonacci lattice, a well-known quasiperiodic system, and Rice-Mele model. We find that these quasiperiodic systems show topological charge pumping with a multi-level behavior due to the fractal nature of the Fibonacci lattice. Such multilevel pumping behaviors can be understood by a real space renormalization group analysis.

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“…TBG advantages are i) its simplicity, as they are made from a single chemical element, and ii) they have a high degree of manipulation that cuprates doesn't have. In recent years, there has been a significant interest in these phases of matter from a fundamental point of view [5][6][7][8][9][10][11][12][13] but also because they present a lot of possible electronic applications and quantum computing advantages [13,14]. There is also an interest connection between topological phases, edge states, semimetals and fractional quantum Hall effect (FQHE) [15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect

Navarro-Labastida¹,

Naumis²

2022

Preprint

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Flat band electronic modes in twisted graphene bilayers are responsible for superconducting and other highly correlated electron-electron phases. Although some hints were known of a possible connection between the quantum Hall effect and zero flat band modes, it was not clear how such connection appears. Here the electronic behavior in twisted bilayer graphene is studied using the chiral model Hamiltonian. As a result it is proved that for high-order magic angles, the zero flat band modes converge into coherent Landau states with a dispersion σ 2 = 1/3α, where α is a coupling parameter that incorporates the twist angle and energetic scales. Then it is proved that the square of the hamiltonian, which is a 2 × 2 matrix operator, turns out to be equivalent to a two-dimensional quantum harmonic oscillator. The interlayer currents between graphene's bipartite lattices are identified with the angular momentum term while the confinement potential is an effective quadratic potential. From there it is proved a limiting quantization rule for high-order magic angles, i.e., αm+1 − αm = (3/2)m where m is the order of the angle. All these results are in very good agreement with numerical calculations.

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Moiré edge states in twisted bilayer graphene and their topological relation to quantum pumping

Cited by 19 publications

References 69 publications

Transport and spectral properties of magic-angle twisted bilayer graphene junctions based on local orbital models

Transport and spectral properties of magic-angle twisted bilayer graphene junctions based on local orbital models

Topological charge pumping in quasiperiodic systems characterized by Bott index

3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect

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