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Register a new userSplitting of the superfluid transition in $^3$He by nematic aerogels
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Authors
I. A. Fomin
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Role of inhomogeneous perturbations of nematic aerogel on the form of the order parameter emerging at the transition of liquid $^3$He in the superfluid state is considered. It is shown that a region of stability of the polar distorted ABM phase can begin right from the transition temperature. The symmetry argument is given, which selects the most favorable aerogel for stabilization of pure polar phase.
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We consider fermionic states bound on domain walls in a Weyl superfluid $^3$He-A and on interfaces between $^3$He-A and a fully gapped topological superfluid $^3$He-B. We demonstrate that in both cases fermionic spectrum contains Fermi arcs which are continuous nodal lines of energy spectrum terminating at the projections of two Weyl points to the plane of surface states in momentum space. The number of Fermi arcs is determined by the index theorem which relates bulk values of topological invariant to the number of zero energy surface states. The index theorem is consistent with an exact spectrum of Bogolubov- de Gennes equation obtained numerically meanwhile the quasiclassical approximation fails to reproduce the correct number of zero modes. Thus we demonstrate that topology describes the properties of exact spectrum beyond quasiclassical approximation.
The discovery of superfluid $^{3}$He in high porosity silica aerogels, and subsequent experimental and theoretical work, have led to a better general understanding of quasiparticle scattering from impurities in unconventional pairing systems. It is immensely helpful for understanding impurity effects in the case of superfluid $^{3}$He that the structure of its order parameter is well-established. An overview of impurity effects is presented with emphasis on those experiments which have a quantitative interpretation in terms of theoretical models for homogeneous and inhomogeneous scattering. The latter can account successfully for most experimental results.
We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B-phase of superfluid $^3$He in 98% porosity aerogel down to the zero temperature limit for a wide range of pressures at zero magnetic field. The absolute attenuation was determined by direct transmission of sound pulses. Compared to the bulk fluid, our results revealed a drastically different behavior in attenuation, which is consistent with theoretical accounts with gapless excitations and a collision drag effect.
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.
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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