A new cubic Hall viscosity in three-dimensional topological semimetals

The interplay between geometry and topology has been a guiding paradigm for recent developments in condensed matter physics. In chiral crystals, it has been shown that crystal symmetries can stabilize exotic multifold fermions, where 3,4, or 6 bands become degenerate at high-symmetry momenta. Due to the crucial role of spatial geometry in stabilizing these degeneracies, it is natural to expect that multifold fermions will also exhibit nontrivial responses to geometric deformation. In this talk, we explore this issue for the first time by examining the viscous response of a threefold degenerate "spin-1" fermion in the cubic (magnetic) space group P2₁3 (198), with time-reversal symmetry breaking chiral magnetism. We derive the non-dissipative Hall viscosity for a spin-1 fermion following two different approaches. We find that the cubic symmetry of the unperturbed Hamiltonian allows for the appearance of a new, fundamentally three dimensional nondissipative viscous force.