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The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…

We investigate spin transport in two dimensional ferromagnetic (FTI) and antiferromagnetic (AFTI) topological insulators. In presence of an in plane magnetization AFTI supports zero energy modes, which enables topologically protected edge…

Mesoscale and Nanoscale Physics · Physics 2017-01-26 Sumit Ghosh , Aurelien Manchon

Altermagnets, a novel class of collinear magnetic materials, exhibit unique spin-split band structures, yet topological insulating states in intrinsic altermagnetic systems are rare. Here, we identify monolayer Fe$_2X_2$O ($X$ = Cl, Br, I)…

Materials Science · Physics 2026-01-22 Yong-Kun Wang , Si Li , Shengyuan A. Yang

We propose a theoretical framework to engineer hybrid-order and higher-order topological phases in three-dimensional topological insulators by coupling to $d$-wave altermagnets (AMs). Presence of only $d_{x^2-y^2}$-type AM drives the system…

Mesoscale and Nanoscale Physics · Physics 2026-05-19 Minakshi Subhadarshini , Amartya Pal , Arijit Saha

The integration of intrinsically magnetic and topologically nontrivial two-dimensional materials holds tantalizing prospects for the exotic quantum anomalous Hall insulators and magnetic second-order topological insulators (SOTIs). Compared…

Mesoscale and Nanoscale Physics · Physics 2024-09-24 Zhao Liu , Bing Liu , Yuefeng Yin , Nikhil V. Medhekar

Generally, the topological corner state in two-dimensional second-order topological insulator (2D SOTI) is equivalent to the well-known domain wall state, originated from the mass-inversion between two adjacent edges with phase shift of pi.…

Mesoscale and Nanoscale Physics · Physics 2021-07-14 Gan Zhao , Haimen Mu , Huimin Zhang , Z. F. Wang

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

In two dimensions, intrinsic second-order topological insulators (SOTIs) are characterized by topological corner states that emerge at the intersections of distinct edges with reversed mass signs, enforced by spatial symmetries. Here, we…

Materials Science · Physics 2024-06-21 Z. J. Chen , S. G. Xu , Z. J. Xie , H. Xu , H. M. Weng

Altermagnets are a novel class of materials that combine antiferromagnetic spin ordering with non-relativistic spin splitting (NRSS) in their band structure, making them promising candidates for spintronics applications without requiring…

Strongly Correlated Electrons · Physics 2025-08-12 Niklas Sicheler , Roberto Raimondi , Giorgio Sangiovanni , Lorenzo Del Re

The discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the $d$-dimension insulating bulk is confined to ($d-1$)-dimensions, led to several potential applications. Recently, it…

The scientific interest in two-dimensional topological insulators (2D TIs) is currently shifting from a more fundamental perspective to the exploration and design of novel functionalities. Key concepts for the use of 2D TIs in spintronics…

We consider a metasurface consisting of a square lattice of cylindrical antidots in a two-dimensional topological insulator (2DTI). Each antidot supports a degenerate Kramer's pair of eigenstates formed by the helical topological edge…

Mesoscale and Nanoscale Physics · Physics 2021-10-13 Fedor Nigmatulin , Ivan Shelykh , Ivan Iorsh

Spin-momentum locking plays a fundamental role in spintronics and, more broadly, is an important concept in condensed matter physics. In 2D and 3D, spin-momentum locking typically does not allow spin-conservation because the spin-1/2…

Mesoscale and Nanoscale Physics · Physics 2026-02-05 Yoonseok Hwang , Penghao Zhu , Taylor L. Hughes

We present models of topological insulating Hamiltonians exhibiting intrinsic altermagnetic features, protected by combined three-fold or four-fold rotational symmetries with time-reversal. We demonstrate that the spin Chern number serves…

Mesoscale and Nanoscale Physics · Physics 2026-02-19 Rafael Gonzalez-Hernandez , Bernardo Uribe

Topological Surface States (TSS) represent new types of two dimensional electron systems with novel and unprecedented properties distinct from any quantum Hall-like or spin-Hall effects. Their Z$_2$ topological order can be realized at room…

Mesoscale and Nanoscale Physics · Physics 2014-01-07 M. Zahid Hasan , Su-Yang Xu , David Hsieh , L. Andrew Wray , Yuqi Xia

When interacting spins in condensed matter order ferromagnetically, their ground state wave function is topologically trivial. Nonetheless, in two dimensions, the ferromagnetic state can support spin excitations with nontrivial topology, an…

Mesoscale and Nanoscale Physics · Physics 2021-07-14 Alexander Mook , Sebastián A. Díaz , Jelena Klinovaja , Daniel Loss

Quadrupole phase, as a novel high-order topological phase, exhibits nontrivial gapless states at the boundaries whose dimension is lower than bulk by two. However, this phase has not been observed experimentally in two-dimensional (2D)…

Materials Science · Physics 2022-11-03 Z. H. Li , P. Zhou , Q. H. Yan , X. Y. Peng , Z. S. Ma , L. Z. Sun

Detection and manipulation of electrons' spins are key prerequisites for spin-based electronics or spintronics. This is usually achieved by contacting ferromagnets with metals or semiconductors, in which the relaxation of spins due to…

Materials Science · Physics 2014-11-05 Y. Shiomi , K. Nomura , Y. Kajiwara , K. Eto , M. Novak , Kouji Segawa , Yoichi Ando , E. Saitoh

We establish a unified, symmetry-driven framework that combines the alternating spin splitting of altermagnets with valley topology to realize and electrically interconvert helical and chiral topological phases within a single material…

Mesoscale and Nanoscale Physics · Physics 2026-03-09 Xianzhang Chen , Jiayong Zhang , Bowen Hao , Jiahui Qian , Ziye Zhu , Igor Zutic , Zhenyu Zhang , Tong Zhou

Periodic driving provides a platform to dynamically tailor quantum states of matter, yet its impact on symmetry-protected topological phases remains incompletely understood. Here, we demonstrate that periodic driving enables the realization…