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This paper reviews the confinement-driven phase transitions, and theprediction of superfluid phases with broken time-reversal or translationalsymmetry in thin films. The new phases are a result of particle-hole coherentAndreev scattering processes that create quasiparticle states with energiesinside the superconducting gap. These states cause profound restructuring ofthe 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 ormore physical dimensions $D \sim 10\xi_0$, Andreev bound states can dominateproperties of the superfluid phases, leading to modified experimentalsignatures. They can dramatically change the energy landscape, and drivetransitions into new superfluid phases, that are typically unstable in the bulksuperfluid. On the examples of single-component singlet d-wave superconductor,and triplet multi-component superfluid $^3$He I show how properties ofcondensed phases in restricted geometry depend on the order parameterstructure. I will highlight the connection between Andreev bound states andconfinement-stabilized phases with additional broken symmetries, describerecent progress and open questions in theoretical and experimentalinvestigation of superfluids in confined geometry.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

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