Andreev bound states in superconducting films and confined superfluid ³ He

Abstract

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 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∼10, 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 -wave superconductors to multi-component triplet superfluidHe, 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'.

Spontaneous Helical Order of a Chiral p -Wave Superfluid Confined in Nanoscale Channels

“…and UPt 3 , as well as the cuprates. Indeed theoretical predictions of novel broken translational symmetry phases are reported for d-wave superconductors subject to strong confinement [23,24], and it seems likely that there are more novel broken symmetry phases in multi-component, unconventional superconductors awaiting discovery. Acknowledgements -This research was supported by National Science Foundation Grant DMR-1508730.…”

Thermal transport of helium-3 in a strongly confining channel

“…The stable phase within the channel will influence the nature of the surface excitations. For nonmagnetic specular surfaces a domain wall in the planar distorted B-phases depletes the density of mid-gap low-energy surface bound states 74 . Thus, while we expect that there will be a rich interplay of superfluid phase, domain walls, and superfluid interfaces on the thermal transport under strong confinement, this is beyond the scope of the current experiment, and will be the subject of future investigation.…”

Fragility of surface states in topological superfluid 3He

“…This result can be phenomenologically described in terms of an effective specularity S eff = −0.4. This approaches the condition for maximal pair-breaking S = −1, corresponding to full retroreflection, in which case the phase shift φ experienced by the retro-reflected quasiparticle is φ = π for all incoming/outgoing trajectories and surface-bound states accumulate at zero energy, since the excitation energy is given by E=Δ ¼ ± cosðφ=2Þ 28 , where Δ is the gap along the quasiparticle's trajectory (see density of states calculation as a function of specularity in Fig. 3c).…”

“…Surface scattering dominates the properties under strong confinement. NMR determines the superfluid transition temperature, the pairing state, and the superfluid energy gap 24 , 26 , 27 , the suppression of which under confinement self-consistently determines, through quasiclassical theory 28 , 29 , the density of states of the ABS mid-gap surface excitations.…”