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Crystal symmetry plays a central role in governing a wide range of fundamental physical phenomena. One example is the nonlinear optical second harmonic generation (SHG), which requires inversion symmetry breaking. Here we report a unique…

Mesoscale and Nanoscale Physics · Physics 2019-11-27 Yuwei Shan , Yingguo Li , Di Huang , Qingjun Tong , Wang Yao , Wei-Tao Liu , Shiwei Wu

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…

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…

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

Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes…

Twisted graphene systems have draw significant attention due to the discoveries of various correlated and topological phases. In particular, recently the alternating twisted trilayer graphene is discovered to exhibit unconventional…

Mesoscale and Nanoscale Physics · Physics 2022-06-02 Bo Xie , Shihao Zhang , Jianpeng Liu

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…

The effects of topology and electron-electron interactions on the phase diagram of ABC stacked trilayer graphene (TLG) at the neutrality point are investigated within a weak coupling renormalization group approach. We find that the leading…

Strongly Correlated Electrons · Physics 2012-10-19 Vladimir Cvetkovic , Oskar Vafek

A double moir\'e superlattice can be realized by stacking three layers of atomically thin two-dimensional materials with designer interlayer twisting or lattice mismatches. In this novel structure, atomic reconstruction of constituent…

The ability to identify and characterize spontaneous symmetry breaking is central to our understanding of 2D materials with strong correlation, such as the moir\'e flat bands in magic-angle twisted graphene bilayer and trilayer. In this…

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

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

Symmetry breaking is an effective tool for tuning the transport and topological properties of 2D layered materials. Among these materials, twisted bilayer graphene (TBG) has emerged as a promising platform for new physics, characterized by…

Mesoscale and Nanoscale Physics · Physics 2024-06-06 Cunyuan Jiang , Matteo Baggioli , Qing-Dong Jiang

Twisted graphene moire superlattice has been demonstrated as an exotic platform for investigating correlated states and nontrivial topology. Among the moire family, twisted double bilayer graphene (TDBG) is a tunable flat band system…

We theoretically study the nonlinear optical response of ABC trilayer graphene with inversion symmetry broken by the application of a displacement field perpendicular to the trilayer. We show that rhombohedral trilayer graphene exhibits a…

Mesoscale and Nanoscale Physics · Physics 2025-01-14 Abigail Postlewaite , Arpit Raj , Swati Chaudhary , Gregory A. Fiete

Graphene multilayers exhibit electronic spectra that depend sensitively on both the number of layers and their stacking order. Beyond trilayer graphene, mixed stacking sequences (alternating Bernal and rhombohedral layers) give rise to…

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

The non-interacting energy spectrum of graphene and its bilayer counterpart consists of multiple degeneracies owing to the inherent spin, valley and layer symmetries. Interactions among charge carriers are expected to spontaneously break…

Mesoscale and Nanoscale Physics · Physics 2015-05-20 R. Thomas Weitz , Monica T. Allen , Benjamin E. Feldman , Jens Martin , Amir Yacoby

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

Although most two-dimensional (2D) materials are non-ferroelectric with highly symmetric lattices, symmetry breaking may take place in their bilayers upon certain stacking order, giving rise to so-called sliding ferroelectricity where the…

Mesoscale and Nanoscale Physics · Physics 2023-04-10 Liu Yang , Menghao Wu
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