Spectroscopy of surface Majorana fermions in superfluid ³He-B using a mechanical oscillator

The superfluid ³He-B is a prototype of DIII topological superconductors, which hosts helical Majorana fermions on the surface. As a consequence of the chiral symmetry, Majorana fermions show uniaxially anisotropic magnetic response, and only a particular orientation of a magnetic Zeeman field can generate the mass gap, which is referred to as Majorana Ising spins. Recently, P. Zheng et al. [Phys. Rev. Lett. 117, 195301 (2016)] observed the anomalous damping of a microelectromechanical system (MEMS) device immersed in the superfluid ³He-B. Here we investigate the damping mechanism of a laterally oscillating plate in the topological superfluid ³He, and clarify the roles of surface Majorana fermions. Using the quasiclassical Keldysh transport theory together with a random S-matrix model, we calculate the stress tensor on the surface of a laterally oscillating plate embedded in ³He-B. We demonstrate that the low-temperature behaviors of the damping rate are sensitive to surface specularity and mass gap induced by magnetic Zeeman fields. The power law of the damping rate in low temperatures may provide spectroscopy for the mass gap of surface states and the topological phase transition in the superfluid ³He-B.