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Recent experimental and theoretical investigations demonstrate that twisted trilayer graphene (tTLG) is a highly tunable platform to study the correlated insulating states, ferromagnetism, and superconducting properties. Here we explore the…

Mesoscale and Nanoscale Physics · Physics 2021-11-17 Zewen Wu , Xueheng Kuang , Zhen Zhan , Shengjun Yuan

Moir\'e materials host a wealth of intertwined correlated and topological states of matter, all arising from flat electronic bands with nontrivial quantum geometry. A prominent example is the family of alternating-twist magic-angle graphene…

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 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

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 investigate the band structure and the optical absorption spectrum of twisted bilayer graphenes with changing interlayer bias and Fermi energy simultaneously. We show that the interlayer bias lifts the degeneracy of the superlattice…

Mesoscale and Nanoscale Physics · Physics 2014-10-20 Pilkyung Moon , Young-Woo Son , Mikito Koshino

Studies of twisted moir\'e systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature…

Strongly Correlated Electrons · Physics 2022-12-27 Ming-Rui Li , Ai-Lei He , Hong Yao

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 graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moir\'{e} superlattice. Such superlattices are known to host bulk valley currents at tiny…

Mesoscale and Nanoscale Physics · Physics 2019-09-04 T. M. R. Wolf , J. L. Lado , G. Blatter , O. Zilberberg

The rich physics of magic angle twisted bilayer graphene (TBG) results from the Coulomb interactions of electrons in flat bands of non-trivial topology. While the bands' dispersion is well characterized, accessing their topology remains an…

Mesoscale and Nanoscale Physics · Physics 2026-03-10 F. Mesple , P. Mallet , G. Trambly de Laissardière , C. Dutreix , G. Lapertot , J-Y. Veuillen , V. T. Renard

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

Stacking two graphene layers twisted by the 'magic angle' $\theta \approx 1.1^\circ$ generates flat energy bands, which in turn catalyzes various strongly correlated phenomena depending on filling and sample details. At charge neutrality,…

Strongly Correlated Electrons · Physics 2021-03-24 Alex Thomson , Jason Alicea

We investigate twisted double bilayer graphene (TDBG), a four-layer system composed of two AB-stacked graphene bilayers rotated with respect to each other by a small angle. Our ab initio band structure calculations reveal a considerable…

Mesoscale and Nanoscale Physics · Physics 2020-04-22 Fatemeh Haddadi , QuanSheng Wu , Alex J. Kruchkov , Oleg V. Yazyev

We consider a configuration of three stacked graphene monolayers with equal consecutive twist angles $\theta$. Remarkably, in the chiral limit when interlayer coupling terms between $\textrm{AA}$ sites of the moir\'{e} pattern are neglected…

Strongly Correlated Electrons · Physics 2023-03-29 Fedor K. Popov , Grigory Tarnopolsky

Twisted trilayer graphene (TLG) may be the simplest realistic system so far, which has flat bands with nontrivial topology. Here, we give a detailed calculation about its band structures and the band topology, i.e. valley Chern number of…

Mesoscale and Nanoscale Physics · Physics 2021-03-31 Zhen Ma , Shuai Li , Ya-Wen Zheng , Meng-Meng Xiao , Hua Jiang , Jin-Hua Gao , X. C. Xie

We study the appearance of topological Floquet flat bands in alternating-twist multilayer graphene, which has alternating relative twist angle $\pm\theta$ near the first magic angle. While the system hosts both flat bands and a steep Dirac…

Mesoscale and Nanoscale Physics · Physics 2023-10-24 Yingyi Huang

Two-dimensional atomic crystals can radically change their properties in response to external influences such as substrate orientation or strain, resulting in essentially new materials in terms of the electronic structure. A striking…

For the chiral limit of two sheets of $n$-layer Bernal-stacked graphene established in the Physical Review Letters arXiv:2109.10325 and arXiv:2109.11514, we prove a trichotomy: depending on the twisting angle, we have either (1)…

Mathematical Physics · Physics 2025-08-05 Bryan Li , Mengxuan Yang

In twisted bilayer graphene (TBLG), extremely small deviations from the magic twist angle $\theta_m{\approx}1.08^\circ$ change its electronic structure near the Fermi level drastically, causing a meV-wide flat band to appear or disappear.…

Mesoscale and Nanoscale Physics · Physics 2018-11-26 Xianqing Lin , Dan Liu , David Tománek

Moir\'e structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands.…