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Moir\'e lattices provide a highly tunable platform for exploring the interplay between electronic correlations and band topology. Introducing a second moir\'e pattern extends this paradigm: interference between the two moir\'e patterns…

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle…

Mesoscale and Nanoscale Physics · Physics 2020-07-07 Yi-Wen Liu , Ying Su , Xiao-Feng Zhou , Long-Jing Yin , Chao Yan , Si-Yu Li , Wei Yan , Sheng Han , Zhong-Qiu Fu , Yu Zhang , Qian Yang , Ya-Ning Ren , Lin He

We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer…

Mesoscale and Nanoscale Physics · Physics 2013-04-02 E. Suárez Morell , M. Pacheco , L. Chico , L. Brey

We formulate the chiral decomposition rules that govern the electronic structure of a broad family of twisted $N+M$ multilayer graphene configurations that combine arbitrary stacking order and a mutual twist. We show that at the magic angle…

Mesoscale and Nanoscale Physics · Physics 2024-03-20 ShengNan Zhang , Bo Xie , QuanSheng Wu , Jianpeng Liu , Oleg V. Yazyev

Twisted bilayer graphene (TBG) has been experimentally observed to exhibit almost flat bands when the twisting occurs at certain magic angles. In this letter, we report new results on the continuum model of twisted bilayer graphene and its…

Strongly Correlated Electrons · Physics 2021-04-21 Simon Becker , Mark Embree , Jens Wittsten , Maciej Zworski

The interplay of twist and strain in bilayer graphene enables the formation of moir\'e patterns and narrow bands that host correlated and topological phases. While magic-angle twisted bilayer graphene has been widely studied, strain…

Mesoscale and Nanoscale Physics · Physics 2026-03-10 Federico Escudero , Dong Wang , Pierre A. Pantaleón , Shengjun Yuan , Francisco Guinea , Zhen Zhan

Twisted bilayer graphene has been argued theoretically to host exceptionally flat bands when the angle between the two layers falls within a magic range near 1.1$^\circ$. This is now strongly supported by experiment, which furthermore…

Strongly Correlated Electrons · Physics 2019-07-24 Kasra Hejazi , Chunxiao Liu , Leon Balents

Here we present a theory of mirror-symmetric magic angle twisted trilayer graphene. The electronic properties are described by a Hubbard model with long range tunneling matrix elements. The electronic properties are obtained by solving the…

Mesoscale and Nanoscale Physics · Physics 2026-05-13 Alina Wania Rodrigues , Maciej Bieniek , Daniel Miravet , Pawel Hawrylak

We study the effect of an in-plane magnetic field on the non-interacting dispersion of twisted bilayer graphene. Our analysis is rooted in the chirally symmetric continuum model, whose zero-field band structure hosts exactly flat bands and…

Strongly Correlated Electrons · Physics 2020-05-20 Yves H. Kwan , S. A. Parameswaran , S. L. Sondhi

The unexpected discovery of superconductivity and strong electron correlation in twisted bilayer graphene (TBG), a system containing only sp electrons, is considered as one of the most intriguing developments in two-dimensional materials in…

Mesoscale and Nanoscale Physics · Physics 2025-04-22 Wei-Chen Wang , Feng-Wu Chen , Kuan-Sen Lin , Justin T. Hou , Ho-Chun Lin , Mei-Yin Chou

We investigate the electronic structure of a twisted multilayer graphene system forming a moir\'e pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch…

Mesoscale and Nanoscale Physics · Physics 2019-07-17 Christophe Mora , Nicolas Regnault , B. Andrei Bernevig

The emergence of flat bands and correlated behaviors in 'magic angle' twisted bilayer graphene (tBLG) has sparked tremendous interest, though many aspects of the system are under intense debate. Here we report observation of both…

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly-correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of…

Mesoscale and Nanoscale Physics · Physics 2024-04-22 Cunyuan Jiang , Matteo Baggioli , Qing-Dong Jiang

Magic angle twisted trilayer graphene (TTG) has recently emerged as a new platform to engineer strongly correlated flat bands. Here, we reveal the structural and electronic properties of TTG using low temperature scanning tunneling…

By tuning the angle between graphene layers to specific "magic angles" the lowest energy bands of twisted bilayer graphene (TBLG) can be made flat. The flat nature of the bands favors the formation of collective ground states and, in…

Superconductivity · Physics 2019-12-09 Xiang Hu , Timo Hyart , Dmitry I. Pikulin , Enrico Rossi

Motivated by recent Physical Review Letters of Wang-Liu and Ledwith-Vishwanath-Khalaf, we study Tarnopolsky-Kruchkov-Vishwanath chiral model of two sheets of $n$-layer Bernal stacked graphene twisted by a small angle using the framework…

Mathematical Physics · Physics 2023-11-16 Mengxuan Yang

Twisted bilayer graphene with a twist angle of around 1.1{\deg} features a pair of isolated flat electronic bands and forms a strongly correlated electronic platform. Here, we use scanning tunneling microscopy to probe local properties of…

Twisted bilayer graphene (TBG) near "magic angles" has emerged as a rich platform for strongly correlated states of two-dimensional Dirac semimetals. Here we show that twisted bilayers of thin-film magnetic topological insulators (MTI) with…

Mesoscale and Nanoscale Physics · Physics 2022-09-07 Gaurav Chaudhary , Anton A. Burkov , Olle G. Heinonen

Recent transport studies have demonstrated the great potential of twisted monolayer-bilayer graphene (tMBG) as a new platform to host moir\'e flat bands with a higher tunability than twisted bilayer graphene (tBG). However, a direct…

Mesoscale and Nanoscale Physics · Physics 2024-01-10 Ling-Hui Tong , Qingjun Tong , Li-Zhen Yang , Yue-Ying Zhou , Qilong Wu , Yuan Tian , Li Zhang , Lijie Zhang , Zhihui Qin , Long-Jing Yin

The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $\theta_M…