Shear modulus anomaly of multi-component superconductor: the case of $Mx$Bi$2$Se$_3$

A pair of split superconducting transitions in the presence of a symmetry breaking field is a very definitive signature of multi-component superconductivity[1, 2]. We theoretically study the shear modulus anomaly across such pair of split transitions[3]. The talk will be focused on $M_x$Bi$_2$Se$_3$, a nematic superconductor candidate, for which no experimental confirmation of the split transition has been made so far. We propose that the shear modulus $c_{66}$ must vanish at the lower transition: a very clear signature detectable by experiments.

[1] M. Sigrist and R. Joynt, and T. M. Rice, Phys. Rev. B 36, 5186 (1987)
[2] G. E. Volovik, Pis'ma Zh. Eksp. Teor. Fiz. 48, 39 (1988)
[3] P. T. How and S.-K. Yip, Phys. Rev. B 104, L020506 (2021)