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We propose a new correlated topological state which we call a higher-order topological Mott insulator (HOTMI). This state exhibits a striking bulk-boundary correspondence due to electron correlations. Namely, the topological properties in…

Strongly Correlated Electrons · Physics 2019-11-13 Koji Kudo , Tsuneya Yoshida , Yasuhiro Hatsugai

We demonstrate that HOTIs with the quantization of the quadrupole moments can be realized in the two-dimensional elastic phononic crystals (PnCs). Both one-dimensional (1D) topological edge states and zero-dimensional (0D) topological…

Applied Physics · Physics 2019-09-12 Zhen Wang , Qi Wei , Heng-Yi Xu , Da-Jian Wu

High-order topological insulators (TIs) are a family of recently-predicted topological phases of matter obeying an extended topological bulk-boundary correspondence principle. For example, a two-dimensional (2D) second-order TI does not…

Mesoscale and Nanoscale Physics · Physics 2020-06-17 Haoran Xue , Yahui Yang , Fei Gao , Yidong Chong , Baile Zhang

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals. Despite tremendous…

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by a factor of 2 lower than that of the bulk. Topological states in such insulators may be strongly…

In this work we develop a theoretical framework for the control of corner modes in higher-order topological insulators (HOTIs) featuring long-range hoppings and diverse geometries, enabling precise tunability of their spatial positions.…

Mesoscale and Nanoscale Physics · Physics 2025-09-04 Fang Qin , Rui Chen

Higher-order topological insulators (HOTIs) represent a family of topological phases that go beyond the conventional bulkboundary correspondence. d-dimensional n-th order HOTIs maintain (d - n)-dimensional gapless boundary states (in…

Optics · Physics 2026-02-12 Rujiang Li , Wencai Wang , Yongtao Jia , Ying Liu , Pengfei Li , Boris A. Malomed

The higher-order topological insulator (HOTI) is a new type of topological system which has special bulkedge correspondence compared with conventional topological insulators. In this work, we propose a scheme to realize Floquet HOTI in…

Quantum Gases · Physics 2022-06-29 Ying Lei , Xi-Wang Luo , Shaoliang Zhang

Higher order topological insulators are a new class of topological insulators in dimensions $\rm d>1$. These higher-order topological insulators possess $\rm (d - 1)$-dimensional boundaries that, unlike those of conventional topological…

Mesoscale and Nanoscale Physics · Physics 2021-07-05 Arijit Saha , Arun M. Jayannavar

Higher-order topological insulators (HOTIs) are systems with topologically protected in-gap boundary states localized at their $(d-n)$-dimensional boundaries, with $d$ the system dimension and $n$ the order of the topology. This work…

Mesoscale and Nanoscale Physics · Physics 2021-07-02 Linhu Li , Weiwei Zhu , Jiangbin Gong

The higher order topological insulator (HOTI) has enticed enormous research interests owing to its novelty in supporting gapless states along the hinges of the crystal. Despite several theoretical predictions, enough experimental…

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated…

A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear…

Mesoscale and Nanoscale Physics · Physics 2020-10-09 Guido van Miert , Carmine Ortix

The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, which was previously limited to topological states at boundaries of materials, to those at boundaries of boundaries,…

Mesoscale and Nanoscale Physics · Physics 2020-12-17 Weiwei Zhu , Haoran Xue , Jiangbin Gong , Yidong Chong , Baile Zhang

Topological states nurtures the emergence of devices with unprecedented functions in photonics, plasmonics, acoustics and phononics. As one of the recently discovered members, higher-order topological insulators (HOTIs) have been…

Materials Science · Physics 2021-06-17 Biye Xie , Hai-Xiao Wang , Xiujuan Zhang , Peng Zhan , Jian-Hua Jiang , Minghui Lu , Yanfeng Chen

Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological…

Exploring novel topological matters with exotic quantum states has always been a core issue in the field of condensed matter physics, which can update the understanding of topological phases and broaden the classification of topological…

Mesoscale and Nanoscale Physics · Physics 2025-12-09 Wei Jia , Yuping Tian , Huanhuan Yang , Xiangru Kong , Zhi-Hao Huang , Wei-Jiang Gong , Jun-Hong An

While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…

Disordered Systems and Neural Networks · Physics 2023-11-15 Yu-Liang Tao , Jiong-Hao Wang , Yong Xu

I consider higher-order topological insulator (HOTI) created in chi(2) nonlinear medium and based on two-dimensional generalization of the Su-Schrieffer-Heeger waveguide array, where transition between trivial and topological phases is…

Optics · Physics 2025-03-03 Yaroslav V. Kartashov

Topological insulators~(TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs~(HOTIs) are a…

Mesoscale and Nanoscale Physics · Physics 2024-09-16 Arnob Kumar Ghosh , Tanay Nag , Arijit Saha