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Chiral Anomaly

Chiral AnomalyΒΆ

In a Weyl semimetal with a pair of Weyl nodes of opposite chirality, the number of electrons in the vicinity of each is modified in the presence of electric and magnetic fields via

\(\frac{dn_{R/L}^{3D}}{dt} = \pm \frac{e^2}{h^2} \textbf{E} \cdot \textbf{B}\)

Even in the presence of spatially uniform fields, which may be oriented in an arbitrary direction relative to the separation of the Weyl nodes, the density of electrons at an individual node is not conserved.

It tells us that a single Weyl node, or any set with an unbalanced chirality, is problematic, since it will lead to non-conservation of electric charge. However, if the chirality is balanced, as happens for any lattice realization, the opposite Weyl nodes act as sources and sinks of electrons, leading to nodal (or valley) polarizations, while preserving the total charge. The chiral anomaly appears in any odd spatial dimension.

  • It is one of the measurable properties of materials with Weyl nodes in their band structure.

  • It refers to the charge pumping effect from one Weyl point to the other when electric and magnetic fields are applied parallel to each other.