Quantum transport in topological semimetals under magnetic fields (III)

Abstract

We review our most recent research on quantum transport, organizing the review according to the intensity of the magnetic field and focus mostly on topological semimetals and topological insulators. We first describe the phenomenon of quantum transport when a magnetic field is not present. We introduce the nonlinear Hall effect and its theoretical descriptions. Then, we discuss Coulomb instabilities in 3D higher-order topological insulators. Next, we pay close attention to the surface states and find a function to identify the axion insulator in the antiferromagnetic topological insulator MnBi₂Te₄. Under weak magnetic fields, we focus on the decaying Majorana oscillations which has the correlation with spin−orbit coupling. In the section on strong magnetic fields, we study the helical edge states and the one-sided hinge states of the Fermi-arc mechanism, which are relevant to the quantum Hall effect. Under extremely large magnetic fields, we derive a theoretical explanation of the negative magnetoresistance without a chiral anomaly. Then, we show how magnetic responses can be used to detect relativistic quasiparticles. Additionally, we introduce the 3D quantum Hall effect’s charge-density wave mechanism and compare it with the theory of 3D transitions between metal and insulator driven by magnetic fields.

Graphical abstract

Keywords

topological semimetal / topological insulator / axion insulator / nonlinear Hall effect (NHE) / quantum oscillation / quantum Hall effect (QHE) / charge density wave (CDW)

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Acknowledgements

We thank helpful discussions with Haipeng Sun and Rui Chen. This work was supported by the National Key R&D Program of China (No. 2022YFA1403700), the National Natural Science Foundation of China (No. 11925402), Guangdong province (Nos. 2020KCXTD001 and 2016ZT06D348), and the Science, Technology and Innovation Commission of Shenzhen Municipality (Nos. ZDSYS20170303165926217, JAY20170412152620376, and KYTDPT20181011104202253). The numerical calculations were supported by Center for Computational Science and Engineering of SUSTech.

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