  The effects of strains on the low-energy electronic properties of double-Weyl
phases are studied in solids and cold-atom optical lattices. The principal
finding is that deformations do not couple, in general, to the low-energy
effective Hamiltonian as a pseudoelectromagnetic gauge potential. The response
of an optical lattice to strains is simpler, but still only one of several
strain-induced terms in the corresponding low-energy Hamiltonian can be
interpreted as a gauge potential. Most interestingly, the strains can induce a
nematic order parameter that splits a double-Weyl node into a pair of Weyl
nodes with the unit topological charges. The effects of deformations on the
motion of wavepackets in the double-Weyl optical lattice model are studied. It
is found that, even in the undeformed lattices, the wavepackets with opposite
topological charges can be spatially split. Strains, however, modify their
velocities in a very different way and lead to a spin polarization of the
wavepackets.
