NonAbelian anomalies in multiWeyl semimetals
Abstract
We construct the effective field theory for timereversal symmetrybreaking multiWeyl 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 ) nonAbelian static background gauge field. Such an SU(2 ) field preserves certain crystalline symmetry (fourfold rotational or C_{4} in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra, namely, E ∼(p_{x}^{2+py2) n /2} , but E ∼ p_{z} , for example, where momenta p is measured from the Weyl nodes. Consequently, the effective field theory displays U(1 )×SU(2 ) nonAbelian anomalies, yielding the anomalous Hall effect, its nonAbelian 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 fieldtheoretic descriptions of MWSMs of arbitrary monopole charge n (featuring n copies of the Fermi arc surface states), predict signatures of nonAbelian anomaly in tabletop experiments, and pave the way to explore the structure of anomalies for multifold fermions, transforming under arbitrary halfinteger or integer spin representations.
 Publication:

Physical Review Research
 Pub Date:
 January 2020
 DOI:
 10.1103/PhysRevResearch.2.013007
 arXiv:
 arXiv:1905.02189
 Bibcode:
 2020PhRvR...2a3007D
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 21 pages, 10 figures: Accepted version