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...

Complex transverse acoustic impedance of the superfluid (3)He-B was measured at the frequencies of 10 to 80 MHz at 17.0 bar by a cw bridge method. The observed temperature dependence was well explained by the quasiclassical theory with random S-matrix model for a diffusive surface. The temperature dependence was influenced by pair breaking and by quasiparticle density of states at the surface, which was drastically modified from the bulk one by the presence of surface Andreev bound states.

A measurement of the surface Andreev bound states of the superfluid 3 He-B phase under different boundary conditions is presented. Transverse-acoustic impedance spectroscopy was used to determine the bandwidth of the bound states on a wall with various specularities. It was found that the band was broader for larger specularity and filled up the superfluid gap above a critical specularity. Specularity was controlled by coating the wall with thin layers of 4 He and was evaluated separately using acoustic impedance measurement in the normal-fluid phase.

We measure the Brillouin gain spectra in two cores (the central core and one of the outer cores) of a ~3-m-long, silica-based, 7-core multi-core fiber (MCF) with incident light of 1.55 μm wavelength, and investigate the Brillouin frequency shift (BFS) and its dependence on strain and temperature. The BFSs of both the cores are ~10.92 GHz, and the strain- and temperature-dependence coefficients of the BFS in the central core are 484.8 MHz/% and 1.08 MHz/°C, respectively, whereas those in the outer core are 516.9 MHz/% and 1.03 MHz/°C. All of these values are not largely different from those in a silica single-mode fiber, which is expected because the cores are basically composed of the same material (silica). We then analyze the difference in structural deformation between the two cores when strain is applied to the fiber, and show that it does not explain the difference in the BFS dependence of strain in this case. The future prospect on distributed strain and temperature sensing based on Brillouin scattering in MCFs is finally presented.