Topological superfluids under engineered nanofluidic confinement: new order parameters and exotic excitations

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Experiments on liquid helium-three near the absolute zero of temperature have played a key role in the development of many central concepts in condensed matter physics. The discovery of superfluid 3He gave us the first p-wave superfluid, a model for unconventional superconductivity, in which the pairing breaks the symmetry of the parent normal metal. Since that time the international programme of materials discovery has thrown up many new unconventional superconductors. And formally the phases of superfluid 3He can be regarded as a quantum vacua, with parallels in particle physics and cosmology [see "The Universe in a Helium Droplet", G.E.Volovik].Recently the topology (in momentum space) of condensed matter systems has been widely applied as a powerful scheme for their classification, alongside the concept of broken symmetry. The simple truths of topology (eg a sphere's surface cannot be continuously deformed into that of a torus) have a powerful impact when applied to complex interacting quantum systems, by pointing to phenomena that must be there, independent of microscopic details; robust protection is conferred by the inviolable constraints of topology. This may lead to electronic devices whose operation relies on the laws of quantum mechanics in a way immune to environmental disturbance, a vision that is supported by Microsoft's Station Q and associated programmes.In this programme we will study the topological superfluidity of helium-three confined in regular nanofabricated geometries, as a model system to further our understanding of topological quantum matter. Our experiments will exploit the recent technical breakthroughs we have made in quantum nanofluidics, and the development of sensitive NMR techniques based on the detection of the precessing magnetic signal by SQUIDs (Superconducting Quantum Interference Devices).Confinement of superfluid 3He in a slab-like cavity of thickness of order the diameter of the Cooper pairs, has a profound effect on the superfluid order and is expected to stabilize new superfluid states of matter. The compressibility of 3He allows the pair diameter to be pressure-tuned, varying the effective confinement. Regular geometries can be fabricated with well-characterized surfaces, which can be tuned in situ by plating with a helium-4 film. This exquisite geometrical control and tuneability, coupled to the ideal material qualities of superfluid 3He, and highly developed microscopic models provide a rigorous theory-experiment interface. Phases with different topologies are expected to be stable under different conditions, and we will map the effect of our new control parameter, confinement, on these phases. We will quantify the role of disorder, arising from surface roughness, and the importance of quantum size effects. These topological superfluids support novel excitations at the faces or edges of the cavity, at domain walls and vortices. The precise character of these excitations depends on whether the superfluid ground state preserves or breaks time reversal symmetry. At the surface of the B-phase they are propagating Majorana fermions, and we will search for these as part of the project.This project has a strong international collaborative dimension, both experimental and theoretical, closely partnering with Cornell and Northwestern in the USA, and PTB (Berlin) in Germany, and exploiting our membership of the European Microkelvin Collaboration. We will connect with other programmes on topological quantum matter in the UK and internationally, enhanced by the Hubbard Theory Consortium, through its visitors programmes and workshops.The project is expected to lead to fundamental insights into topological quantum matter and topological superfluidity/superconductivity in particular. It will drive the innovation of new instrumentation at the new frontier combining ultra-low temperatures and nanoscience, and new SQUID NMR techniques of broad applicability.