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Register a new userSurface Specific Heat of $^{3}$He and Andreev Bound States
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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.
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Porous aerogel is a source of elastic scattering in superfluid 3He and modifies the properties of the superfluid, suppressing the transition temperature and order parameter. The specific heat jumps for the B-phase of superfluid 3He in aerogel have been measured as a function of pressure and interpreted using the homogeneous and inhomogeneous isotropic scattering models. The specific heat jumps for other p-wave states are estimated for comparison.
The specific heat of superfluid $^{3}$He, disordered by a silica aerogel, is found to have a sharp discontinuity marking the thermodynamic transition to superfluidity at a temperature reduced from that of bulk $^{3}$He. The magnitude of the discontinuity is also suppressed. This disorder effect can be understood from the Ginzburg-Landau theory which takes into account elastic quasiparticle scattering suppressing both the transition temperature and the amplitude of the order parameter. We infer that the limiting temperature dependence of the specific heat is linear at low temperatures in the disordered superfluid state, consistent with predictions of gapless excitations everywhere on the Fermi surface.
We study theoretically the topological surface states (TSSs) and the possible surface Andreev bound states (SABSs) of Cu$_{x}$Bi$_{2}$Se$_{3}$ which is known to be a topological insulator at $x=0$. The superconductivity (SC) pairing of this compound is assumed to have the broken spin-rotation symmetry, similar to that of the A-phase of $^{3}$He as suggested by recent nuclear-magnetic resonance experiments. For both spheroidal and corrugated cylindrical Fermi surfaces with the hexagonal warping terms, we show that the bulk SC gap is rather anisotropic; the minimum of the gap is negligibly small as comparing to the maximum of the gap. This would make the fully-gapped pairing effectively nodal. For a clean system, our results indicate the bulk of this compound to be a topological superconductor with the SABSs appearing inside the bulk SC gap. The zero-energy SABSs which are Majorana fermions, together with the TSSs not gapped by the pairing, produce a zero-energy peak in the surface density of states (SDOS). The SABSs are expected to be stable against short-range nonmagnetic impurities, and the local SDOS is calculated around a nonmagnetic impurity. The relevance of our results to experiments is discussed.
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.
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.
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