Anomalous transport properties of Dirac and Weyl semimetals

Abstract

In this review we discuss a wide range of topological properties of electron quasiparticles in Dirac and Weyl semimetals. Their nontrivial topology is quantified by a monopole-like Berry curvature in the vicinity of Weyl nodes, as well as by the energy and momentum space separations between the nodes. The momentum separation, which is also known as the chiral shift, is one of the key elements of this review. We show that it can be dynamically generated in Dirac materials in a background magnetic field. We also pay a special attention to various forms of interplay between the background electromagnetic fields and the topological characteristics of Dirac and Weyl semimetals. In particular, we discuss their signature features in the transport of the electric and chiral charges, heat, as well as the quantum oscillations associated with the Fermi arc states. The origin of the dissipative transport of the Fermi arc states is critically examined. Finally, a consistent chiral kinetic theory for the description of Weyl semimetals is reviewed and its applications are demonstrated.

25 pages, 7 multi-panel figures; submitted to the special issue of the Low Temperature Physics journal devoted to the 90th anniversary of A. A. Abrikosov

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• Magneto-Transport in a Chiral Fluid from Kinetic Theory
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• Electronic properties of strained double-Weyl systems
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• Dilepton production from chirally asymmetric matter
• Holographic Charged Fluid with Chiral Electric Separation Effect
• An extended $R_{{\Psi }_m}^{(2)}(\Delta S_2)$ correlator for detecting and characterizing the Chiral Magnetic Wave
• Anomalous Gurzhi effect
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