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Symmetry breaking governs most fascinating phenomena in crystals, such as ferroelectricity, nonlinear optics, piezoelectricity, ferromagnetism, and superconductivity. In two-dimensional materials, a wide variety of tuning knobs presents…

Mesoscale and Nanoscale Physics · Physics 2024-07-11 Wenqiang Zhou , Jiannan Hua , Naitian Liu , Jing Ding , Hanxiao Xiang , Wei Zhu , Shuigang Xu

Graphene, defined as a single atomic plane of graphite, is a semimetal with small overlap between the valence and the conduction bands. The stacking of graphene up to several atomic layers can produce diverse physical properties, depending…

Materials Science · Physics 2019-02-08 Jiliang Zhang , Guangcun Shan

Stacking order plays a crucial role in determining the crystal symmetry and has significant impacts on electronic, optical, magnetic, and topological properties. Electron-phonon coupling, which is central to a wide range of intriguing…

Second harmonic generation (SHG) is a powerful optical tool for identifying non-centrosymmetric crystalline structures. Here, we analyze SHG in multilayer graphenes (MLG), with a focus on its dependence on the stacking order, encapsulation…

Mesoscale and Nanoscale Physics · Physics 2026-03-25 Patrick Johansen Sarsfield , Takaaki V. Joya , Takuto Kawakami , Mikito Koshino , Vladimir Fal'ko

Optical spectroscopy based on second-order nonlinearity is a critical technique for characterizing two-dimensional (2D) crystals as well as bioimaging and quantum optics. It is generally believed that second-harmonic generation (SHG) in…

Mesoscale and Nanoscale Physics · Physics 2026-01-14 Haoning Tang , Zhitong Ding , Tianyi Ruan , Zeyu Hao , Kenji Watanabe , Takashi Taniguchi , Haozhe Wang , Ali Javey , Feng Wang , Yuan Cao

The crystallographic stacking order in multilayer graphene plays an important role in determining its electronic structure. In trilayer graphene, rhombohedral stacking (ABC) is particularly intriguing, exhibiting a flat band with an…

Materials Science · Physics 2017-06-12 Changhua Bao , Wei Yao , Eryin Wang , Chaoyu Chen , José Avila , Maria C. Asensio , Shuyun Zhou

Stackings in graphene have a pivotal role in properties to be discussed in the future, as seen in the recently found superconductivity of twisted bilayer graphene. Beyond bilayer graphene, the stacking order of multilayer graphene can be…

Mesoscale and Nanoscale Physics · Physics 2022-12-12 Raúl Guerrero-Avilés , Marta Pelc , Fabian Geisenhof , Thomas Weitz , Andrés Ayuela

A striking feature of bilayer graphene is the induction of a significant band gap in the electronic states by the application of a perpendicular electric field. Thicker graphene layers are also highly attractive materials. The ability to…

Mesoscale and Nanoscale Physics · Physics 2012-02-21 Chun Hung Lui , Zhiqiang Li , Kin Fai Mak , Emmanuele Cappelluti , Tony F. Heinz

In graphite crystals, layers of graphene reside in three equivalent, but distinct, stacking positions typically referred to as A, B, and C projections. The order in which the layers are stacked defines the electronic structure of the…

Few-layer graphene (FLG) has been predicted to exist in various crystallographic stacking sequences, which can strongly influence the electronic properties of FLG. We demonstrate an accurate and efficient method to characterize stacking…

Materials Science · Physics 2011-02-01 Chun Hung Lui , Zhiqiang Li , Zheyuan Chen , Paul V. Klimov , Louis E. Brus , Tony F. Heinz

Recent studies have reported emergent ferroelectric behavior in twisted or moir\'e-engineered graphene-based van der Waals heterostructures, yet the microscopic origin of this effect remains under debate. Pristine mono- or few-layer…

We observed distinct interlayer shear mode Raman spectra for trilayer graphene with ABA and ABC stacking order. There are two rigid-plane shear-mode phonon branches in trilayer graphene. We found that ABA trilayers exhibit pronounced Raman…

Mesoscale and Nanoscale Physics · Physics 2015-06-19 Chun Hung Lui , Zhipeng Ye , Courtney Keiser , Eduardo B. Barros , Rui He

The extrinsic stacking sequence based on intrinsic crystal symmetry in multilayer two-dimensional materials plays a significant role in determining their electronic and optical properties. Compared with Bernal-stacked (ABA) multilayer…

Mesoscale and Nanoscale Physics · Physics 2024-08-20 Zuo Feng , Wenxuan Wang , Yilong You , Yifei Chen , Kenji Watanabe , Takashi Taniguchi , Chang Liu , Kaihui Liu , Xiaobo Lu

We construct a continuum model of twisted trilayer graphene using {\it ab initio} density-functional-theory calculations, and apply it to address twisted trilayer electronic structure. Our model accounts for moir\'e variation in site…

Mesoscale and Nanoscale Physics · Physics 2021-07-27 Chao Lei , Lukas Linhart , Wei Qin , Florian Libisch , Allan H. MacDonald

We develop a theory for interlayer pairing of chiral electrons in graphene materials which results in an unconventional superconducting (S) state with s-wave spin-triplet order parameter. In a pure bilayer graphene, this superconductivity…

Mesoscale and Nanoscale Physics · Physics 2012-12-10 Mir Vahid Hosseini , Malek Zareyan

We systematically investigate the nonlinear photogalvanic effect in few-layer graphene with various stacking orders, including AA- and AB-stacked bilayers, and AAA-, ABA-, and ABC-stacked trilayers. Using a tight-binding model to describe…

Mesoscale and Nanoscale Physics · Physics 2026-04-13 Zhaohang Li , Kainan Chang , Haoyu Li , Yuxuan Gao , Wei Xin , Jinluo Cheng , Haiyang Xu

The crystal structure of a material plays an important role in determining its electronic properties. Changing from one crystal structure to another involves a phase transition which is usually controlled by a state variable such as…

Few layer graphene (FLG) has been recently intensively investigated for its variable electronic properties defined by a local atomic arrangement. While the most natural layers arrangement in FLG is ABA (Bernal) stacking, a metastable ABC…

In tetralayer graphene, three inequivalent layer stackings should exist, however, only rhombohedral (ABCA) and Bernal (ABAB) stacking have so far been observed. The three stacking sequences differ in their electronic structure, with the…

We report markedly different transport properties of ABA- and ABC-stacked trilayer graphenes. Our experiments in double-gated trilayer devices provide evidence that a perpendicular electric field opens an energy gap in the ABC trilayer,…

Mesoscale and Nanoscale Physics · Physics 2011-11-08 S. H. Jhang , M. F. Craciun , S. Schmidmeier , S. Tokumitsu , S. Russo , M. Yamamoto , Y. Skourski , J. Wosnitza , S. Tarucha , J. Eroms , C. Strunk
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