Non-Abelian anomalies in multi-Weyl semimetals

Renato M. A. Dantas; Francisco Peña-Benitez; Bitan Roy; Piotr Surówka

doi:10.1103/PhysRevResearch.2.013007

paper

Non-Abelian anomalies in multi-Weyl semimetals

arXiv:1905.02189 · doi:10.1103/PhysRevResearch.2.013007

Abstract

We construct the effective field theory for time-reversal symmetry breaking multi-Weyl semimetals (mWSMs), composed of a single pair of Weyl nodes of (anti-)monopole charge $n$ , with $n = 1, 2, 3$ in crystalline environment. From both the continuum and lattice models, we show that a mWSM with $n > 1$ can be constructed by placing $n$ flavors of linearly dispersing simple Weyl fermions (with $n = 1$ ) in a bath of an $S U (2)$ non-Abelian static background gauge field. Such an $S U (2)$ field preserves certain crystalline symmetry (four-fold rotational or $C_{4}$ in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra (namely, $E \sim (p_{x}^{2} + p_{y}^{2})^{n /2}$ , but $E \sim ∣ p_{z} ∣$ , for example, where momenta $p$ is measured from the Weyl nodes). Consequently, the effective field theory displays $U (1) \times S U (2)$ non-Abelian anomaly, yielding anomalous Hall effect, its non-Abelian generalization, and various chiral conductivities. The anomalous violation of conservation laws is determined by the monopole charge $n$ and a specific algebraic property of the $S U (2)$ Lie group, which we further substantiate by numerically computing the regular and "isospin" densities from the lattice models of mWSMs. These predictions are also supported from a strongly coupled (holographic) description of mWSMs. Altogether our findings unify the field theoretic descriptions of mWSMs of arbitrary monopole charge $n$ (featuring $n$ copies of the Fermi arc surface states), predict signatures of non-Abelian anomaly in table-top experiments, and pave the route to explore anomaly structures for multi-fold fermions, transforming under arbitrary half-integer or integer spin representations.

arXiv comment21 pages, 10 figures: Accepted version

Non-Abelian anomalies in multi-Weyl semimetals

Abstract

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