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The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…

Mesoscale and Nanoscale Physics · Physics 2011-10-24 Su-Yang Xu , Y. Xia , L. A. Wray , D. Qian , Shuang Jia , J. H. Dil , F. Meier , J. Osterwalder , B. Slomski , H. Lin , R. J. Cava , M. Z. Hasan

Topology-driven nonlinear light-matter effects open up new paradigms for both topological photonics and nonlinear optics. Here, we propose to achieve high-efficiency second-harmonic generation in a second-order photonic topological…

Optics · Physics 2021-12-02 Yafeng Chen , Zhihao Lan , Jensen Li , Jie Zhu

We evidence the possibility for coherent electrical manipulation of the spin orientation of topologically protected edge states in a low-symmetry quantum spin Hall insulator. By using a combination of ab-initio simulations, symmetry-based…

Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap are protected by time-reversal symmetry. When a proper kind of antiferromagnetic long range order is established in a…

Mesoscale and Nanoscale Physics · Physics 2015-05-19 Jing Wang , Rundong Li , Shou-Cheng Zhang , Xiao-Liang Qi

We study the higher-order topological insulators at finite temperature based on a generalized real-space quadrupole moment, which extends the ground state expectations to ensemble averages. Our study reveals that chiral symmetry alone…

Mesoscale and Nanoscale Physics · Physics 2025-08-04 Yiting Deng , Yan He

Quadrupole insulators are a class of second-order topological insulators (SOTIs) that host zero-dimensional corner states within a two-dimensional bulk. Despite their unique properties, their realization in electronic systems on realistic…

Mesoscale and Nanoscale Physics · Physics 2026-05-13 Haiyue Huang , Prineha Narang , Ioannis Petrides

We demonstrate that rotation symmetry is not a necessary requirement for the existence of fractional corner charges in Cn-symmetric higher-order topological crystalline insulators. Instead, it is sufficient to have a latent rotation…

Mesoscale and Nanoscale Physics · Physics 2025-02-26 L. Eek , M. Röntgen , A. Moustaj , C. Morais Smith

We demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods. By tuning a single geometry parameter, the photonic…

Optics · Physics 2021-09-01 Hai-Xiao Wang , Li Liang , Bin Jiang , Junhui Hu , Xiancong Lu , Jian-Hua Jiang

Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form…

Applied Physics · Physics 2024-04-25 Zhoufei Liu , Pei-Chao Cao , Liujun Xu , Guoqiang Xu , Ying Li , Jiping Huang

Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…

Mesoscale and Nanoscale Physics · Physics 2021-05-21 Jiong-Hao Wang , Yan-Bin Yang , Ning Dai , Yong Xu

Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order…

Strongly Correlated Electrons · Physics 2026-05-26 Aswin Parayil Mana , Yabo Li , Hiroki Sukeno , Tzu-Chieh Wei

We study disorder effects in a two-dimensional system with chiral symmetry and find that disorder can induce a quadrupole topological insulating phase (a higher-order topological phase with quadrupole moments) from a topologically trivial…

Mesoscale and Nanoscale Physics · Physics 2021-02-05 Yan-Bin Yang , Kai Li , L. -M. Duan , Yong Xu

Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing…

Different from the traditional bulk-edge correspondence principle, the discovery of higher-order topological states has generated widespread interest. In a second-order, two-dimensional elastic wave topological insulator, the fluctuation…

Applied Physics · Physics 2023-01-10 Ze Ma , Yang Liu , Yu-Xin Xie , Yue-Sheng Wang

Recently, the theory of quantized dipole polarization has been extended to account for electric multipole moments, giving rise to the discovery of multipole topological insulators (TIs). Both two-dimensional (2D) quadrupole and…

Mesoscale and Nanoscale Physics · Physics 2020-09-16 Weixuan Zhang , Deyuan Zou , Wenjing He , Jiacheng Bao , Qingsong Pei , Houjun Sun , Xiangdong Zhang

Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a…

Mesoscale and Nanoscale Physics · Physics 2025-12-12 Yu-Long Zhang , Cheng-Ming Miao , Qing-Feng Sun , Jian-Jun Liu , Ying-Tao Zhang

Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we…

Mesoscale and Nanoscale Physics · Physics 2020-05-14 Z. -X. Li , Yunshan Cao , Peng Yan , X. R. Wang

Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…

Mesoscale and Nanoscale Physics · Physics 2016-08-24 Anton Quelle , Emilio Cobanera , Cristiane Morais Smith

Quantized bulk quadrupole moment has unveiled a nontrivial boundary state, exhibiting lower-dimensional topological edge states and simultaneously hosting the in-gap corner modes of zero dimension. All state-of-the-art strategies for…

Mesoscale and Nanoscale Physics · Physics 2022-09-22 Guoqiang Xu , Xue Zhou , Jing Wu , Cheng-Wei Qiu

Efficient control of phonons is crucial to energy-information technology, but limited by the lacking of tunable degrees of freedom like charge or spin. Here we suggest to utilize crystalline symmetry-protected pseudospins as new quantum…

Mesoscale and Nanoscale Physics · Physics 2019-09-12 Yizhou Liu , Yong Xu , Wenhui Duan