Abstract
Weyl semimetals are three-dimensional crystalline systems where pairs of bands touch at points in momentum space, termed Weyl nodes, that are characterized by a definite topological charge: the chirality. Consequently, they exhibit the Adler-Bell-Jackiw anomaly, which in this condensed-matter realization implies that the application of parallel electric () and magnetic () fields pumps electrons between nodes of opposite chirality at a rate proportional to . We argue that this pumping is measurable via nonlocal transport experiments, in the limit of weak internode scattering. Specifically, we show that as a consequence of the anomaly, applying a local magnetic field parallel to an injected current induces a valley imbalance that diffuses over long distances. A probe magnetic field can then convert this imbalance into a measurable voltage drop far from source and drain. Such nonlocal transport vanishes when the injected current and magnetic field are orthogonal and therefore serves as a test of the chiral anomaly. We further demonstrate that a similar effect should also characterize Dirac semimetals—recently reported to have been observed in experiments—where the coexistence of a pair of Weyl nodes at a single point in the Brillouin zone is protected by a crystal symmetry. Since the nodes are analogous to valley degrees of freedom in semiconductors, the existence of the anomaly suggests that valley currents in three-dimensional topological semimetals can be controlled using electric fields, which has potential practical “valleytronic” applications.
- Received 14 September 2013
DOI:https://doi.org/10.1103/PhysRevX.4.031035
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Published by the American Physical Society
Popular Summary
We study two different examples of “topological semimetals,” which have been proposed as three-dimensional analogs of graphene whose electronic excitations are described by the Weyl and Dirac equations, respectively. The former have been predicted to occur in a host of materials, inspiring ongoing experimental efforts; the latter appear to have been recently observed in experiments using and . Our focus is on a particular aspect of these topological semimetals: their quantum anomaly. We show that the anomaly has a directly measurable effect on the transport of charge in real materials.
We study both Dirac and Weyl semimetals, where the former can simply be thought of as two copies of the latter. We focus on , given its relatively simple crystalline structure. Topological semimetals respond in a peculiar fashion when placed in parallel electric and magnetic fields: Electrons are “pumped” between two distinct Fermi points, reflecting the fact that the symmetry between these points is broken when the quantum-mechanical electrons couple to the external fields. The corresponding anomaly in the Standard Model of particle physics has important consequences, explaining, for instance, why a massless neutral meson can decay into two photons. The quantum anomaly enables electrical currents injected into the system parallel to an external magnetic field to drive internal “valley currents” that describe how the imbalance between Fermi points diffuses through the material. These currents can, in turn, induce electrical currents and voltage drops far away from the original point of injection, when a suitably oriented magnetic field is applied.
Such “nonlocal” electromagnetic responses turn out to be a hallmark of Weyl and Dirac materials and may allow us to probe some aspects of anomaly physics in a tabletop experiment, paving the way for identifying new three-dimensional Weyl and Dirac semimetals.