scholarly journals Realization of topological Mott insulator in a twisted bilayer graphene lattice model

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bin-Bin Chen ◽  
Yuan Da Liao ◽  
Ziyu Chen ◽  
Oskar Vafek ◽  
Jian Kang ◽  
...  
Keyword(s):  
Lattice Model ◽  
Large Scale ◽  
Mott Insulator ◽  
Bilayer Graphene ◽  
Magic Angle ◽  
Coulomb Interactions ◽  
Stripe Phase ◽  
Density Matrix Renormalization ◽  
Correlated Electron ◽  
Twisted Bilayer Graphene

AbstractMagic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.

scholarly journals Flat band carrier confinement in magic-angle twisted bilayer graphene

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nikhil Tilak ◽  
Xinyuan Lai ◽  
Shuang Wu ◽  
Zhenyuan Zhang ◽  
Mingyu Xu ◽  
...  
Keyword(s):  
Twist Angle ◽  
Bilayer Graphene ◽  
Scanning Tunneling Spectroscopy ◽  
Scanning Tunneling ◽  
Flat Band ◽  
Magic Angle ◽  
Energy Bands ◽  
Carrier Confinement ◽  
Correlated Electron ◽  
Twisted Bilayer Graphene

AbstractMagic-angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomogeneity which can drastically modify the local potential landscape. This potential disorder is distinct from the twist angle variation which has been studied elsewhere. Here, by using low temperature scanning tunneling spectroscopy and planar tunneling junction measurements, we demonstrate that flat bands in twisted bilayer graphene can amplify small doping inhomogeneity that surprisingly leads to carrier confinement, which in graphene could previously only be realized in the presence of a strong magnetic field.

scholarly journals Gate-defined Josephson junctions in magic-angle twisted bilayer graphene

2021 ◽  
Author(s):  
Folkert K. de Vries ◽  
Elías Portolés ◽  
Giulia Zheng ◽  
Takashi Taniguchi ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Josephson Junctions ◽  
Bilayer Graphene ◽  
Magic Angle ◽  
Twisted Bilayer Graphene

scholarly journals DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Paul Eugenio ◽  
Ceren Dag
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Ground States ◽  
Bilayer Graphene ◽  
Chern Number ◽  
Strong Interactions ◽  
Time Reversal Symmetry ◽  
Density Matrix Renormalization ◽  
Topological Quantum ◽  
Twisted Bilayer Graphene

Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern=\pm1=±1), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry (\mathbb{Z}_2ℤ2). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle|++⋯+⟩ or all negative |{--\cdots-}\rangle|−−⋯−⟩. If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2)SU(2) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1ν=1 spin-\frac{1}{2}12 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

Raman spectra of twisted bilayer graphene close to the magic angle

2D Materials ◽  
2022 ◽  
Author(s):  
Tiago Campolina Barbosa ◽  
Andreij C. Gadelha ◽  
Douglas A. A. Ohlberg ◽  
Kenji Watanabe ◽  
Takashi Taniguchi ◽  
...  
Keyword(s):  
Raman Spectra ◽  
Laser Excitation ◽  
Bilayer Graphene ◽  
Geometrical Model ◽  
Excitation Wavelength ◽  
Magic Angle ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Excitation Laser ◽  
Twisted Bilayer Graphene

Abstract In this work, we study the Raman spectra of twisted bilayer graphene samples as a function of their twist-angles (θ), ranging from 0.03º to 3.40º, where local θ are determined by analysis of their associated moiré superlattices, as imaged by scanning microwave impedance microscopy. Three standard excitation laser lines are used (457, 532, and 633 nm wavelengths), and the main Raman active graphene bands (G and 2D) are considered. Our results reveal that electron-phonon interaction influences the G band's linewidth close to the magic angle regardless of laser excitation wavelength. Also, the 2D band lineshape in the θ < 1º regime is dictated by crystal lattice and depends on both the Bernal (AB and BA) stacking bilayer graphene and strain soliton regions (SP) [1]. We propose a geometrical model to explain the 2D lineshape variations, and from it, we estimate the SP width when moving towards the magic angle.

scholarly journals Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene

Nature ◽  
2019 ◽  
Vol 573 (7772) ◽  
pp. 91-95 ◽  
Author(s):  
Yuhang Jiang ◽  
Xinyuan Lai ◽  
Kenji Watanabe ◽  
Takashi Taniguchi ◽  
Kristjan Haule ◽  
...  
Keyword(s):  
Rotational Symmetry ◽  
Charge Order ◽  
Bilayer Graphene ◽  
Magic Angle ◽  
Twisted Bilayer Graphene
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