The nonclassical rotational inertia fraction of the identical cylindrical solid 4He below 300 mK is studied at 496 and 1173 Hz by a double resonance torsional oscillator. Below 35 mK, the fractions are the same at sufficiently low rim velocities. Above 35 mK, the fraction is greater for the higher than the lower mode. The dissipation peak of the lower mode occurs at a temperature approximately 4 mK lower than that of the higher mode. The drive dependence of the two modes shows that the reduction of the fraction is characterized by critical velocity, not amplitude or acceleration.

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We measured the transverse acoustic impedance of superfluid 3He-B with a wall coated by several layers of 4He. The coating is known to enhance the specularity in quasiparticle scattering by the wall. We found a new anomaly, a bump and a peak, in the temperature dependence of the transverse acoustic impedance. This agrees with a theoretical calculation using a partially specular wall boundary condition. The new anomaly is shown to arise from a change in the surface density of states by coating and the scattering of thermally occupied surface bound states to other states. The change is towards the density of states of Majorana cone in the specular limit.

The superfluid3 He B phase, one of the oldest unconventional fermionic condensates experimentally realized, is recently predicted to support Majorana fermion surface states. Majorana fermion, which is characterized by the equivalence of particle and antiparticle, has a linear dispersion relation referred to as the Majorana cone. We measured the transverse acoustic impedance Z of the superfluid 3 He B phase changing its boundary condition and found a growth of peak in Z on a higher specularity wall. Our theoretical analysis indicates that the variation of Z is induced by the formation of the cone-like dispersion relation and thus confirms the important feature of the Majorana fermion in the specular limit. KEYWORDS: superfluid3 He, surface Andreev bound states, Majorana fermions, Majorana cone, acoustic impedanceSurface Andreev bound states (SABS) of the superfluid 3 He B phase are receiving renewed attention as ''edge states'' of a three-dimensional (3D) time reversal invariant topological superfluid.1-9) Topological superfluids and superconductors are characterized by a non-trivial topological number in the gapped bulk state and a gapless edge state on their edges or surfaces. SABS of the superfluid 3 He B phase can be regarded as Majorana fermions as they satisfy the Majorana condition, i.e., a particle and its antiparticle are equivalent, because the degrees of freedom of the bound states are halved. When a surface is specular, linear dispersions are predicted for Majorana fermions, 10) which have been recently referred to as a Majorana cone. 4,5) We measured the transverse acoustic impedance Z of the superfluid 3 He B phase changing its boundary condition up to practically specular scattering. The observed variation of Z is well reproduced by theoretical analysis and is shown to be induced by the formation of the cone-like dispersion relation of SABS at higher specularities. This provides an evidence of the existence of the Majorana cone in superfluid 3 He B in the specular limit. Superfluid 3 He is a well established spin-triplet p-wave superfluid where the B phase is the realization of the BalianWerthamer state, which breaks the relative spin-orbit symmetry.11,12) The surface Majorana states of the 3 He B phase should exhibit peculiar features such as a surface spin current and an anisotropic magnetic response.5,7-9) Under the specular scattering boundary condition of the surface, SABS with a finite energy are not degenerate, and have a dispersion relation linear to the momentum, which takes the shape of a 2D cone for massless Dirac fermions. In the spin-triplet p-wave pairing system, the annihilation operator of the negative energy state is equivalent to the creation operator of the positive energy state. Hence, only the positive energy cone, which is called a Majorana cone, is physical.4,5) To date, Majorana surface fermion states have been discussed mostly on smooth surfaces (specular scattering limit). However, intriguing problems are to elucidate how the Majorana cone transforms as the roughness of th...