Electric response of Majorana fermions in topological crystalline superconductors

Majorana fermions appear on the surface of topological superconductors and are usually stable against any perturbations. On the other hand, when the topological superconductors have time-reversal symmetry, a pair of Majorana fermions, called the Majorana Kramers pair, appears on the surface, which is able to respond to a magnetic field. Since the magnetic structure of the Majorana Kramers pair has an Ising type magnetic anisotropy, it responds to a magnetic field applied in a specific direction, Recently, the relationship among the magnetic response, crystalline symmetry, and pairing symmetry of superconductors has been clarified. Thus, the magnetic response provides useful information about the superconducting mechanism.

In this talk, we extend the above theory to the case of a double Majorana Kramers pair, which is able to respond to an electric perturbation. Establishing the classification of the double Majorana Kramers pair in terms of the wallpaper groups, we clarify all possible electric multipole responses. In addition, we reveal the relationship between the electric multipole responses and pairing symmetry. As an example, we demonstrate a specific irreducible representation of a uniform strain yields gap in the double Majorana Kramers pair for topological crystalline superconductor candidate Sr3SnO. This highlights the validity of electric detection of pairing symmetry.