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The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may…

Mesoscale and Nanoscale Physics · Physics 2015-08-31 Chao-Xing Liu , Shou-Cheng Zhang , Xiao-Liang Qi

Ultra-thin 3D topological insulators provide a stage to study the surface physics of such materials by minimizing the bulk contribution. Further, the experimentally verified snowflake like structure of the Fermi surface leads to a hexagonal…

Mesoscale and Nanoscale Physics · Physics 2016-03-02 Anirudha Menon , Debashree Chowdhury , Banasri Basu

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena.…

Strongly Correlated Electrons · Physics 2024-09-10 Dechen Zhang , Kuan-Wen Chen , Guoxin Zheng , Fanghang Yu , Mengzhu Shi , Yuan Zhu , Aaron Chan , Kaila Jenkins , Jianjun Ying , Ziji Xiang , Xianhui Chen , Lu Li

The anomalous Hall effect is caused by magnetic textures such as skyrmions. We derive an analytical formula of the Hall conductivity on the surface of a topological insulator up to third order in magnetization,…

Mesoscale and Nanoscale Physics · Physics 2021-04-30 Terufumi Yamaguchi , Ai Yamakage

The quantum spin Hall effect has been observed in topological insulators using spin-orbit coupling as the probe, but it has not yet been observed in a metal. An experiment is proposed to measure the quantum spin Hall effect of an electron…

Mesoscale and Nanoscale Physics · Physics 2022-10-21 Aiying Zhao , Qiang Gu , Timothy J. Haugan , Thomas J. Bullard , Richard A. Klemm

Photocurrent acts as one of measurable responses of material to light, which has proved itself to be crucial for sensing and energy harvesting. Topological semimetals with gapless energy dispersion and abundant topological surface and bulk…

Mesoscale and Nanoscale Physics · Physics 2023-04-21 Po-Hsin Shih , Thi-Nga Do , Godfrey Gumbs , Danhong Huang , Hsin Lin , Tay-Rong Chang

In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…

Quantum Gases · Physics 2022-09-14 Philipp Hauke , Iacopo Carusotto

The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the…

Mesoscale and Nanoscale Physics · Physics 2009-11-10 K. Ishikawa , T. Aoyama , Y. Ishizuka , N. Maeda

Using a two-dimensional square lattice Heisenberg model with a Rashba-type Dzyaloshinskii-Moriya interaction, we demonstrate that chiral spin fluctuations can give rise to a thermal Hall effect in the absence of any static spin texture or…

Mesoscale and Nanoscale Physics · Physics 2021-06-23 Caitlin Carnahan , Yinhan Zhang , Di Xiao

Emerging magnetic fields related to the presence of topologically protected spin textures such as skyrmions are expected to give rise to additional, topology-related contributions to the Hall effect. In order to doubtlessly identify this…

The Hall effect, in which current flows perpendicular to an applied electrical bias, has played a prominent role in modern condensed matter physics over much of the subject's history. Appearing variously in classical, relativistic and…

Materials Science · Physics 2021-07-08 Libor Smejkal , Allan H. MacDonald , Jairo Sinova , Satoru Nakatsuji , Tomas Jungwirth

In this paper, we present the theoretical predication of a thermospin Hall effect, in which a transverse spin current can be generated in semiconductors in the presence of spin-orbit coupling by a frequency-dependent longitudinal…

Mesoscale and Nanoscale Physics · Physics 2008-02-05 Zhongshui Ma

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

Measurement techniques based upon the Hall effect are invaluable tools in condensed matter physics. When an electric current flows perpendicular to a magnetic field, a Hall voltage develops in the direction transverse to both the current…

Charged particles exhibit the Hall effect in the presence of magnetic fields. Analogously, ferromagnetic skyrmions with non-zero topological charges and finite fictitious magnetic fields exhibit the skyrmion Hall effect, which is…

The Hall effect usually occurs when the Lorentz force acts on a charge current in a conductor in the presence of perpendicular magnetic field. On the other hand, neutral quasi-particles such as phonons and spins can carry heat current and…

Materials Science · Physics 2010-08-12 Y. Onose , T. Ideue , H. Katsura , Y. Shiomi , N. Nagaosa , Y. Tokura

Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluids in the presence of a counterflow, the influence of a vortex tangle on various thermodynamic phenomena in quantum liquids is studied. Using…

Soft Condensed Matter · Physics 2024-08-02 Sergey K. Nemirovskii

Fourier's law dictates that heat flow is usually parallel to the applied temperature gradient. However, under a high magnetic field, heat flow carried by both electrons in conductors and phonons in insulators can be deflected, a phenomenon…

Strongly Correlated Electrons · Physics 2026-05-28 Zhe Cui , Haoran Fan , Wenjiang Zhou , Xianghong Jin , Yuchen Gu , Da Ma , Cong Xiao , Hua Jiang , Xincheng Xie , Bai Song , Yuan Li , Xi Lin

We develop a theory for the electrical and thermal transverse linear response functions such as the Hall, Nernst and thermal Hall effects in magnetic materials that harbor topological spin textures like skyrmions. In addition to the…

Mesoscale and Nanoscale Physics · Physics 2025-08-05 Zachariah Addison , Lauren Keyes , Mohit Randeria

The quantum anomalous Hall effect refers to the quantization of Hall effect in the absence of applied magnetic field. The quantum anomalous Hall effect is of topological nature and well suited for field-free resistance metrology and…

Mesoscale and Nanoscale Physics · Physics 2022-09-21 Hang Chi , Jagadeesh S. Moodera