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Register a new userCritical Velocity in the Presence of Surface Bound States in Superfluid $^3$He-B
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A microelectromechanical oscillator with a gap of 1.25 $mu$m was immersed in superfluid $^3$He-B and cooled below 250 $mu$K at various pressures. Mechanical resonances of its shear motion were measured at various levels of driving force. The oscillator enters into a nonlinear regime above a certain threshold velocity. The damping increases rapidly in the nonlinear region and eventually prevents the velocity of the oscillator from increasing beyond the critical velocity which is much lower than the Landau critical velocity. We propose that this peculiar nonlinear behavior stems from the escape of quasiparticles from the surface bound states into the bulk fluid.
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Topological superfluid $^3$He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid $^3$He within a cavity of height comparable to the Cooper pair diameter. We precisely determine the superfluid transition temperature $T_{mathrm{c}}$ and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasi-classical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of $T_{mathrm{c}}$, corresponding to an increased density of low energy bound states.
The superfluid $^3$He formed by spin-triplet $p$-wave Cooper pairs is a typical topological superfluid. In the superfluid $^3$He B-phase, several kinds of vortices classified by spatial symmetries $P_1$, $P_2$, and $P_3$ are produced, where $P_1$ is inversion symmetry, $P_2$ is magnetic reflection symmetry, and $P_3$ is magnetic $pi$-rotation symmetry. We have calculated the vortex bound states by the Bogoliubov-de Gennes theory and the quasiclassical Eilenberger theory, and also clarified symmetry protection of the low energy excitations by the spatial symmetries. On the symmetry protection, $P_3$ symmetry plays a key role which gives two-fold degenerate Majorana zero modes. Then, the bound states in the most symmetric $o$ vortex with $P_1$, $P_2$, and $P_3$ symmetries and in $w$ vortex with $P_3$ symmetry have the symmetry protected degenerate Majorana zero modes. On the other hand, zero energy modes in $v$ vortex, which is believed to be realized in the actual B-phase, are not protected, and in consequence become gapped by breaking axial symmetry. The excitation gap may have been observed as the variation of critical velocity. We have also suggested an experimental setup to create $o$ vortex with Majorana zero modes by a confinement and a magnetic field.
High resolution measurements of the specific heat of liquid $^{3}$He in the presence of a silver surface have been performed at temperatures near the superfluid transition in the pressure range of 1 to 29 bar. The surface contribution to the heat capacity is identified with Andreev bound states of $^{3}$He quasiparticles that have a range of half a coherence length.
The superfluid $^3$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.
The mechanical resonance properties of a micro-electro-mechanical oscillator with a gap of 1.25 $mu$m was studied in superfluid $^3$He-B at various pressures. The oscillator was driven in the linear damping regime where the damping coefficient is independent of the oscillator velocity. The quality factor of the oscillator remains low ($Qapprox 80$) down to 0.1 $T_c$, 4 orders of magnitude less than the intrinsic quality factor measured in vacuum at 4 K. In addition to the Boltzmann temperature dependent contribution to the damping, a damping proportional to temperature was found to dominate at low temperatures. We propose a multiple scattering mechanism of the surface Andreev bound states to be a possible cause for the anomalous damping.
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