Very thin films of 3He: A new phase

Fragility of surface states in topological superfluid 3He

Superfluid ³He, 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 superfluids and 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 ³He within a cavity of height D comparable to the Cooper pair diameter ξ₀. We precisely determine the superfluid transition temperature T_c and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasiclassical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of T_c, corresponding to an increased density of low energy bound states.

Surface states in topological quantum matter are protected by their band structure. Here, on confined superfluid ³He as a model for topological superconductors, the authors report experimental evidence on the fragility of surface Andreev bound states with respect to the details of surface scattering.

Stabilized Pair Density Wave via Nanoscale Confinement of Superfluid ^{3}He

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 state.

Andreev bound states in superconducting films and confined superfluid 3He

This paper reviews confinement-driven phase transitions in superconductors and Bardeen-Cooper-Schrieffer superfluids, and the appearance in thin films of new phases that break the time-reversal or translational symmetry. The origins of the new phases are closely tied to the Andreev scattering processes involving particle-hole conversions that create surface quasiparticle states with energies inside the superconducting gap. Restructuring of the low-energy spectrum in the surface region of several coherence lengths ξ₀ results in large spatial variations of the superconducting order parameter. In confined geometry, such as slabs, films, pores or nano-dots, with one or more physical dimensions D∼10ξ₀, the Andreev bound states can dominate properties of a superconductor, leading to modified experimental signatures. They can significantly change the energy landscape, and drive transitions into new superconducting phases. The new phases are expected in a variety of materials, from singlet d-wave superconductors to multi-component triplet superfluid ³He, but properties of the new phases will depend on the symmetry of the parent state. I will highlight the connection between the Andreev surface states and confinement-stabilized phases with additional broken symmetries, describe recent progress and open questions in the theoretical and experimental investigation of superfluids in confined geometry.This article is part of the theme issue 'Andreev bound states'.

Fabrication of microfluidic cavities using Si-to-glass anodic bonding

We demonstrate the fabrication of ∼1.08 μm deep microfluidic cavities with characteristic size as large as 7 mm × 11 mm or 11 mm diameter, using a silicon-glass anodic bonding technique that does not require posts to act as separators to define cavity height. Since the phase diagram of ³He is significantly altered under confinement, posts might act as pinning centers for phase boundaries. The previous generation of cavities relied on full wafer-bonding which is more prone to failure and requires dicing post-bonding, whereas these cavities are made by bonding a pre-cut piece of Hoya SD-2 glass to a patterned piece of silicon in which the cavity is defined by etching. Anodic bonding was carried out at 425 °C with 200 V, and we observe that pressurizing the cavity to failure (>30 bars pressure) results in glass breaking, rather than the glass-silicon bond separation. In this article, we discuss the detailed fabrication of the cavity, its edges, and details of the junction between the coin silver fill line and the silicon base of the cavity that enables a low internal-friction joint. This feature is important for mass coupling torsional oscillator experimental assays of the superfluid inertial contribution where a high quality factor (Q) improves frequency resolution. The surface preparation that yields well-characterized smooth surfaces to eliminate pinning sites, the use of transparent glass as a cover permitting optical access, low temperature capability, and attachment of pressure-capable ports for fluid access may be features that are important in other applications.

The A-B transition in superfluid helium-3 under confinement in a thin slab geometry

The influence of confinement on the phases of superfluid helium-3 is studied using the torsional pendulum method. We focus on the transition between the A and B phases, where the A phase is stabilized by confinement and a spatially modulated stripe phase is predicted at the A–B phase boundary. Here we discuss results from superfluid helium-3 contained in a single 1.08-μm-thick nanofluidic cavity incorporated into a high-precision torsion pendulum, and map the phase diagram between 0.1 and 5.6 bar. We observe only small supercooling of the A phase, in comparison to bulk or when confined in aerogel, with evidence for a non-monotonic pressure dependence. This suggests that an intrinsic B-phase nucleation mechanism operates under confinement. Both the phase diagram and the relative superfluid fraction of the A and B phases, show that strong coupling is present at all pressures, with implications for the stability of the stripe phase.

Superfluid helium-3 provides a clean testing ground for the understanding of quantum phases and their transitions. Here the authors show that when helium is confined in a nanofluidic cavity supercooling across the first-order A–B transition is suppressed, indicating an intrinsic nucleation mechanism.

Onset of Superfluidity in ^{3}He Films

We elucidate, for the first time, the overall behavior of the onset temperature of superfluidity in ^{3}He films for a wide range of film thicknesses d between 0.06 and 10  μm by taking advantage of the tunability of d implemented using microfabricated devices. We observe a suppression of the onset temperature of superfluidity T_{c}^{f} in a film from the bulk transition temperature as d decreases. In particular, T_{c}^{f} is strongly suppressed when d approaches the coherence length (∼77  nm). The observed T_{c}^{f} as a function of d is similar to that expected from the quasiclassical theory, but it unexpectedly deviates from the theoretical value by several percent when 0.5≲d≲5  μm.

Symmetry protected topological superfluid (3)He-B

Owing to the richness of symmetry and well-established knowledge of bulk superfluidity, the superfluid (3)He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of (3)He in a multifaceted manner, including symmetry considerations, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the (3)He-B confined in a slab geometry. The (3)He-B under a magnetic field is separated to two different sub-phases: the symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of the (3)He nucleus. It is also demonstrated that odd-frequency even-parity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt3 and Rashba superconductors as examples.

Crystalline order in superfluid (3)He films

We predict an inhomogeneous phase of superfluid (3)He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, D(c2)(T) < D < D(c1)(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D(c2) approximately 9 xi (T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at D(c1) approximately 13 xi (T).

Surface specific heat of 3He and Andreev bound states

High resolution measurements of the specific heat of liquid 3He in the presence of a silver surface have been performed at temperatures near the superfluid transition in the pressure range of 1-29 bar. The surface contribution to the heat capacity is identified with Andreev bound states of quasiparticles that have a range of half a coherence length.