Geometric transport signatures and 3D Hall viscosity in strained multi-Weyl semimetals

The minimal coupling of strain to Dirac and Weyl semimetals, and its modelling as a pseudogauge field has been extensively studied, resulting in several proposed topological transport signatures. We study the effects of strain on higher winding number Weyl semimetals and show that strain is not a pseudogauge field for any winding number larger than 1. Instead, the application of strain splits the higher winding number Weyl nodes and produces an anisotropic Fermi surface. Analogous to the theory of nematicity in quantum Hall fluids in (2+1)D, we construct field theories in (3+1)D describing strained multi-Weyl semimetals and evaluate strain-induced Hall viscosity for higher winding numbers in (3+1)D. The resulting transport signatures due to strain are thus strongly associated with the deformed geometry of the Weyl nodes rather than their topology. We discuss these transport signatures that are dependent on the covariant coupling of the strain tensor to the geometric tensor of the Weyl nodes. Thus, we show that in multi-Weyl semimetals, strain produces geometric signatures rather than topological signatures.