Shear modulus anomaly of unconventional superconductors in a symmetry breaking field

Using Ginzburg-Landau formalism, we theoretically study the isothermal shear modulus anomaly of an unconventional superconductor with a two-component order parameter, where the superconducting transition is split by a symmetry-breaking field. Experimental signatures are proposed for both chiral and nematic superconductors. Particularly striking is the vanishing of C-66 across the lower transition to a nematic superconducting state. Our findings can guide future experiments and shed new light on materials such as Sr2RuO4 and MxBi2Se3.