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Two-dimensional Dirac semimetals with a single massless Dirac cone exhibit the parity anomaly. Usually, such a kind of anomalous topological semimetallic phase in real materials is unstable where any amount of disorder can drive it into a…

Mesoscale and Nanoscale Physics · Physics 2023-09-14 Zhen Ning , Xianyong Ding , Dong-Hui Xu , Rui Wang

The pursuit of understanding parity anomaly in condensed matter systems has led to significant advancements in both theoretical and experimental research in recent years. In this study, we explore the parity anomaly of massless Dirac…

Mesoscale and Nanoscale Physics · Physics 2024-03-14 Huan-Wen Wang , Bo Fu , Shun-Qing Shen

A semimagnetic topological insulator -- a heterostructure combining a topological insulator with a ferromagnet -- exhibits a half-quantized Hall effect, characterized by a quantized Hall conductance of $\frac{1}{2}\frac{e^{2}}{h}$ (where…

Disordered Systems and Neural Networks · Physics 2025-10-30 Shi-Hao Bi , Bo Fu , Shun-Qing Shen

The interplay between topological materials and local symmetry breaking gives rise to diverse topological quantum phenomena. A notable example is the parity anomalous semimetal (PAS), which hosts a single unpaired gapless Dirac cone with a…

Materials Science · Physics 2026-04-20 Binbin Wang , Jiayuan Hu , Bo Fu , Jiaqi Li , Yunchuan Kong , Kai-Zhi Bai , Shun-Qing Shen , Di Xiao

A three-dimensional topological insulator features a two-dimensional surface state consisting of a single linearly-dispersive Dirac cone. Under broken time-reversal symmetry, the single Dirac cone is predicted to cause half-integer…

Mesoscale and Nanoscale Physics · Physics 2022-02-03 M. Mogi , Y. Okamura , M. Kawamura , R. Yoshimi , K. Yasuda , A. Tsukazaki , K. S. Takahashi , T. Morimoto , N. Nagaosa , M. Kawasaki , Y. Takahashi , Y. Tokura

The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far…

Mesoscale and Nanoscale Physics · Physics 2022-03-03 Bo Fu , Jin-Yu Zou , Zi-Ang Hu , Huan-Wen Wang , Shun-Qing Shen

The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by…

Mesoscale and Nanoscale Physics · Physics 2017-06-12 Rui Chen , Dong-Hui Xu , Bin Zhou

Condensed matter realization of a single Dirac cone of fermions in two dimensions is a long-standing issue. Here we report the discovery of a single gapless Dirac cone of half-quantized Hall conductance in a magnetically-doped topological…

Mesoscale and Nanoscale Physics · Physics 2023-04-12 Jin-Yu Zou , Rui Chen , Bo Fu , Huan-Wen Wang , Zi-Ang Hu , Shun-Qing Shen

The half-quantized Hall conductance is characteristic of quantum systems with parity anomaly. Here we investigate topological and transport properties of a class of parity anomalous semimetals, in which massive Dirac fermions coexist with…

Mesoscale and Nanoscale Physics · Physics 2022-05-18 Jin-Yu Zou , Bo Fu , Huan-Wen Wang , Zi-Ang Hu , Shun-Qing Shen

Electric conductivities may reveal the topological and magnetic properties of band structures in solids, especially for two-dimensional unpaired Dirac fermions. In this work, we evaluate the longitudinal and Hall conductivity for unpaired…

Mesoscale and Nanoscale Physics · Physics 2025-11-17 Bo Fu , Kai-Zhi Bai , Shi-Hao Bi , Shun-Qing Shen

We investigate a transition between a two-dimensional topological insulator conduction state, characterized by a conductance $G=2$ (in fundamental units $e^2/h$) and a Chern insulator with $G=1$, induced by polarized magnetic impurities.…

Mesoscale and Nanoscale Physics · Physics 2015-08-12 Laurent Raymond , Alberto D. Verga , Arnaud Demion

In magnetically doped thin-film topological insulators, aligning the magnetic moments generates a quantum anomalous Hall phase supporting a single chiral edge state. We show that as the system de-magnetizes, disorder from randomly oriented…

Mesoscale and Nanoscale Physics · Physics 2019-07-30 Arbel Haim , Roni Ilan , Jason Alicea

We study the influence of disorder on the topological transition from a two-dimensional Dirac semi-metal to an insulating state. This transition is described as a continuous merging of two Dirac points leading to a semi-Dirac spectrum at…

Mesoscale and Nanoscale Physics · Physics 2013-07-26 David Carpentier , Andrei A. Fedorenko , Edmond Orignac

The half-quantized anomalous Hall conductance (AHC) in topological materials is a condensed matter physics realization of the parity anomaly of (2+1) quantum field theory and an important challenge for both theoretical and experimental…

Mesoscale and Nanoscale Physics · Physics 2026-04-14 Shahid Sattar , Roman Stepanov , Alexander Tyner , M. F. Islam , A. H. MacDonald , C. M. Canali

Topological matter is a trending topic in condensed matter: From a fundamental point of view it has introduced new phenomena and tools, and for technological applications, it holds the promise of basic stable quantum computing. Similarly,…

Disordered Systems and Neural Networks · Physics 2016-08-29 Eduardo V. Castro , Raphael de Gail , M. Pilar López-Sancho , María A. H. Vozmediano

Recent advances in constructing synthetic dimension provide a powerful tool for exploring exotic topological states of matter in high dimensions. Here we report that the parity anomaly and associated \textit{half-integer} quantized Hall…

Mesoscale and Nanoscale Physics · Physics 2025-05-15 Xian-Hao Wei , Xi-Wang Luo , Guang-Can Guo , Zheng-Wei Zhou

The half-quantized Hall phase represents a unique metallic or semi-metallic state of matter characterized by a fractional quantum Hall conductance, precisely half of an integer $\nu$ multiple of $e^{2}/h$. Here we demonstrate the existence…

Mesoscale and Nanoscale Physics · Physics 2024-09-25 Bo Fu , Shun-Qing Shen

Weyl semimetals are gapless quasi-topological materials with a set of isolated nodal points forming their Fermi surface. They manifest their quasi-topological character in a series of topological electromagnetic responses including the…

Mesoscale and Nanoscale Physics · Physics 2016-02-05 Hassan Shapourian , Taylor L. Hughes

We report the discovery of the half-quantized mirror Hall effect, a novel quantum-anomaly induced by mirror symmetry in a strong topological insulator (TI) film. These films are known to host a pair of gapless Dirac cones associated with…

Mesoscale and Nanoscale Physics · Physics 2024-02-06 Bo Fu , Kai-Zhi Bai , Shun-Qing Shen

Quantum anomalous Hall effect, with a trademark of dissipationless chiral edge states for electronics/spintronics transport applications, can be realized in materials with large spin-orbit coupling and strong intrinsic magnetization. After…

Mesoscale and Nanoscale Physics · Physics 2021-01-05 Muhammad Nadeem , Alex R. Hamilton , Michael S. Fuhrer , Xiaolin Wang
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