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Register a new userStabilized Pair Density Wave via Nanoscale Confinement of Superfluid $^3$He
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Superfluid $^3$He under nanoscale confinement has generated significant interest due to the rich spectrum of phases with complex order parameters that may be stabilized. Experiments have uncovered a variety of interesting phenomena, but a complete picture of superfluid $^3$He under confinement has remained elusive. Here, we present phase diagrams of superfluid $^3$He under varying degrees of uniaxial confinement, over a wide range of pressures, which elucidate the progressive stability of both the $A$-phase, as well as a growing region of stable pair density wave (PDW) state.
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Recent advances in experiment and theory suggest that superfluid $^3$He under planar confinement may form a pair-density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wavevectors, of possibly square or hexagonal symmetry. In this work, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landaus theory of the liquid-solid transition. A soft-mode instability at finite wavevector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wavevectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.
Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demonstrate that the transition from the FFLO to the normal state as a function of temperature or increased Fermi surface splitting is not a direct one. Instead the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pair-density-wave state is very robust and exists for much larger fields and temperatures than the FFLO state.
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 report that spin supercurrents in magnetic superconductors and superconductor/ferromagnetic insulator bilayers can induce the Dzyaloshinskii-Moriya interaction which strength is proportional to the superconducting order parameter amplitude. This effect leads to the existence of inhomogeneous parity-breaking ground states combining the chiral magnetic helix and the pair density wave orders. The formation of such states takes place via the penetration of chiral domain walls at the threshold temperature below the superconducting transition. We find regimes with both the single and the re-entrant transitions into the inhomogeneous states with decreasing temperature. The predicted hybrid chiral states can be found in the existing structures with realistic parameters and materials combinations.
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.
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