Topological mesoscopic superfluidity of 3He

Helium remains liquid down to the absolute zero of temperature through a combination of relatively weak interatomic interactions and quantum zero point motion. It provides models for studying systems of strongly interacting bosons (4He) and fermions (3He). These materials have played a key role in the development of concepts central to condensed matter physics: Bose-Einstein condensation; macroscopic quantum physics; topological phase transitions; the Landau Fermi liquid theory of electrons in metals; unconventional superconductivity; topological quantum matter. The richest system is superfluid 3He (recognized in the 1996 and 2003 Nobel Prizes), the conceptual reach of which is described by Volovik in terms of a "3He-centric universe", conceptually linked to most major fields of physics.

Condensed matter systems feature in every modern technology. The development of this technology has relied on the discovery and creation of new materials with new phases and often unanticipated properties, as well as hybrid devices which combine these materials, increasingly on the nanoscale.

Recently the understanding of new phases solely in terms of symmetry breaking has been shown to be inadequate in some cases. This is the notion of topological quantum matter (2016 Nobel Prize). Two important classes of quantum matter are at the centre of attention: topological insulators and topological superconductors. Usual insulators do not conduct electricity, because of an energy gap between filled and empty energy bands. But in a topological insulator the momentum space topology of the band structure necessarily gives rise to conducting surface excitations. On the other hand, as a metal is cooled into its superconducting state, a gap emerges. Topological superconductors also support surface/edge excitations, and there are substantial efforts to identify materials that are bulk topological superconductors.

This project will exploit superfluid 3He, known to support two distinct topological superfluid phases in bulk, establishing the new research direction of topological mesoscopic superfluidity. Under nanoscale confinement, this material provides a unique model for topological superconductivity. The subtle interplay between symmetry and topology in these materials is an open question. Our approach will be to confine 3He in precisely engineered geometries to create hybrid nanostructures, allowing a degree of control that is unprecedented. Confinement and periodic structures, with liquid pressure as a tuning parameter of Cooper pair diameter, will induce new superfluid phases, for which the order parameter symmetry will be inferred from nuclear magnetic resonance. These materials will be building blocks for hybrid mesoscopic superfluid systems.

Excitations emerge at surfaces/edges/interfaces of the topological superfluid. As well as the interface with inert matter, where we can tune surface scattering in situ, stepped confinement in hybrid structures will create intra-fluid interfaces of the highest quality. Surface and edge spin currents in time reversal invariant superfluid 3He-B will be investigated by NMR and their coupling to confined Anderson-Higgs order parameter collective modes, as well as nano-wires of diameter similar to that of Cooper pairs. Our ambition is to detect non-local response of the surface Majorana modes. Edge states in chiral superfluid 3He-A will be investigated by a predicted anomalous Hall effect in mass and thermal transport. Interface states will be investigated by thermal transport.

This project has a strong international collaborative dimension, including partnerships with Cornell, NIST and PTB (Berlin). Partnerships with theorists from the USA, Europe and Japan are central to the design and interpretation of experiments. Partnerships within the scientific instruments industry will deliver short-medium term impact from the technical developments central to this project.

Who will benefit?
Topologically protected quantum computing is an ambitious but important long term challenge in quantum technology. The fundamental understanding of topological superconductivity is key to establishing the feasibility of routes to topologically protected quantum computing using such materials. With materials science advances in unconventional superconductivity we can also anticipate future devices based on thin films of these materials with potentially new functionality.

Our fundamental research drives forward the development of state-of-the-art research capacity. These developments in instrumentation measurement systems directly benefit the scientific instruments industry in the short-medium term, especially those focussed on cryogenics, nanoscience and superconducting technologies, widening its customer base. This is fostered by the global reach of UK industry in this sector. In addition new experimental methods, for example the measurement of temperature and new NMR methods, impact on society through National Measurement Institutes.

Collaboration between the UK, mainland Europe and leading groups in the USA, both theoretical and experimental, as well as strong links with Asia increases the opportunity for international impact. We contribute to the scientific society through work for international funding agencies, scientific academies, and globally via IUPAP.

The general public, including young people tend to be excited and motivated by laboratory-based fundamental science at one of Nature's frontiers, and the technical challenges we meet.

How will they benefit?
Advances in the fundamental understanding of topological superconductivity will be underpinned by the research on topological mesoscopic superfluid 3He as a model system. The propagation of these ideas by theorists across discipline boundaries through networking, workshops, will play a key role. The topological classification of condensed matter is a universal scheme, so advances in understanding on model systems will enter the canon of the subject, and are essential for long-term technological progress.

In the short term we expect to continue to export highly trained manpower to industry. This research, at the frontier of the subject, combines new techniques in ultralow temperature physics new measurement techniques, advances in nanofluidics, and crucially a robust confrontation between theory and experiment. Individuals trained in these skills and expertise, equipped with rigorous scientific methodology, are an important resource enhancing economic competitiveness.

Instrumentation development plays a central role in the proposed research. We will work towards short-term impact in: cryogen-free nuclear demagnetization platforms; advances in noise thermometry; definition of the Kelvin; improved heat exchangers; applications of novel superconducting devices to NMR (with potential future applications in medicine).

What will be done to ensure that they benefit?
This proposal includes a number of Project Partnerships. Collaborations are well established with the scientific instruments industry (Oxford Instruments Nanoscience), and here we establish a new partnership with York Instruments.

We have long-term partnerships with National Measurement Institutes, including: strategic partnership with NPL; Project Partnership with PTB. Membership of European Microkelvin Platform with arrangements for technology exchange, innovation management and public engagement both supports our impact agenda, and helps us target areas where we can make a unique contribution. Nationally, impact on Quantum Technology will be enhanced by the new UK Centre of Excellence for superconducting and hybrid quantum systems at Royal Holloway.

Finally, we will develop our public engagement strategy, supported by our dedicated Physics Outreach Officer, through talks, videos, posters, news stories, and enhanced on-line presence.