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 $SU(2)$ non-Abelian static background gauge field. Such an $SU(2)$ 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, $E \sim (p^2_x + p^2_y)^{n/2}$, but $E \sim |p_z|$, for example, where momenta ${\bf p}$ is measured from the Weyl nodes). Consequently, the effective field theory displays $U(1) \times SU(2)$ 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 $SU(2)$ 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.
Highlights
Anomalies are traditionally studied in the realm of relativistic field theories that are pertinent in high-energy physics [1,2,3,4,5,6,7,8]
For the sake of concreteness, we focus on the minimal model for time-reversal symmetry-breaking Weyl semimetals, composed of only a single pair ofmonopole of charge n
The lack of Lorentz symmetry yields a complex and rich structure in the theory, which motivated us to find a suitable generalization of these models in order to shed light on the desired physical phenomena
Summary
Anomalies are traditionally studied in the realm of relativistic field theories that are pertinent in high-energy physics [1,2,3,4,5,6,7,8]. In the world of condensed-matter systems an emergent relativistic symmetry results from the quasiparticle spectra that are linear in momentum, but at low energies This is the quintessential feature of Weyl semimetals, a class of materials where quantum anomaly has been studied theoretically [9,10,11,12,13,14,15,16] and its signature has possibly been observed in experiments [17,18,19,20,21,22,23,24,25,26,27]. For the sake of concreteness, we focus on the minimal model for time-reversal symmetry-breaking Weyl semimetals, composed of only a single pair of (anti)monopole of charge n Given this motivation, we construct an effective field theory for multi-Weyl systems that is always linear in all momenta, but accompanied by a Lorentz violating perturbation, which leads to the multi-Weyl spectrum in the low-energy limit (see Fig. 1). Due to the extensive nature of our study, it is worth pausing at this point to offer an overview of the main results, before delving into the details
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