Quantum Transport in Topological Semimetals
Topological semimetal is a 3D topological state of matter, in which the conduction and valence bands touch at a finite number of Weyl nodes. The Weyl nodes always appear in pairs, and carry opposite chirality. Topological semimetals also host paired monopoles of Berry curvature in momentum space and topologically protected Fermi arcs. More importantly, the chiral anomaly, i.e., the quantization induced breaking of chiral symmetry, is believed to exist in topological semimetals, which has inspired many experiments to explore the quantum transport in topological semimetals. In this talk, I will cover several topics.
(1) Weak antilocalization gives a negative low-temperature magnetoconductivity that competes with the negative magnetoresistance of the “chiral anomaly”. We derived a formula for the weak antilocalization in topological semimetals . The formula has been applied in recent experiments on the first topological Weyl semimetal TaAs . We also figure out the connection between the weak (anti-)localization with the monopole charges and Berry phase, and predict the weak localization in double-Weyl semimetals .
(2) The nontrivial Berry curvature of topological semimetals is expected to give a negative magnetoresistance (positive quadratic-B magnetoconductivity) in parallel magnetic fields. We have experimentally observed the negative magnetoresistance in the topological semimetal Cd3As2 and studied its carrier density dependence .
(3) A linear-B magnetoconductivity in the quantum limit at high fields is expected as a signature of the chiral anomaly, which however was not observed in experiments. We show that the high-field positive magnetoconductivity is not a compelling signature of the chiral anomaly  and find a linear-B magnetoconductivity at half filling of Weyl semimetals .
(4) Topological semimetals are believed to host a nontrivial π Berry phase, leading to a phase shift of ±1/8 in the Shubnikov-de Haas oscillation, which however was not observed in experiments. For Weyl semimetal, we find a non-monotonic phase shift from ±1/8 near the Weyl nodes to ±5/8 at higher Fermi energies. For Dirac semimetal, time-reversal symmetry leads to a discrete phase shift of either ±1/8 or ±5/8. We also find that topological band inversion is one of the origins of beating patterns. Our findings may be helpful for exploring the Berry phase in the Dirac semimetal Cd2As3 and various 3D systems.
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