Andreev Bound States in Superconducting Films and Confined Superfluid He-3

Abstract

This paper reviews the confinement-driven phase transitions, and the prediction of superfluid phases with broken time-reversal or translational symmetry in thin films. The new phases are a result of particle-hole coherent Andreev scattering processes that create quasiparticle states with energies inside the superconducting gap. These states cause profound restructuring of the low-energy spectrum in the surface region of several coherence lengths ${\xi }_0$ with 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 $D\sim 10{\xi }_0$, Andreev bound states can dominate properties of the superfluid phases, leading to modified experimental signatures. They can dramatically change the energy landscape, and drive transitions into new superfluid phases, that are typically unstable in the bulk superfluid. On the examples of single-component singlet d-wave superconductor, and triplet multi-component superfluid ${}^3$He I show how properties of condensed phases in restricted geometry depend on the order parameter structure. I will highlight the connection between Andreev bound states and confinement-stabilized phases with additional broken symmetries, describe recent progress and open questions in theoretical and experimental investigation of superfluids in confined geometry.

25 pages, 9 figures

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Cited by in corpus (14)

• Triangular pair density wave in confined superfluid ${}^3$He
• Breaking time-reversal and translational symmetry at edges of $d$-wave superconductors: microscopic theory and comparison with quasiclassical theory
• Spontaneous helical order of a chiral p-wave superfluid confined in nano-scale channels
• Thermal transport of helium-3 in a strongly confining channel
• Spontaneous symmetry-breaking at surfaces of $d$-wave superconductors: influence of geometry and surface ruggedness
• A-B transition in superfluid ${}^3$He and cosmological phase transitions
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Surface State Dissipation in Confined 3He-A
• Strong-coupling corrections to hard domain walls in superfluid 3He-B
• Controllable enhancement of $p$-wave superconductivity via magnetic coupling to a conventional superconductor
• Chiral superfluid helium-3 in the quasi-two-dimensional limit
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors