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

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.

Who will benefit?
This research contributes to a fundamental understanding of both topological quantum matter and the practical feasibility of topologically protected quantum computing, a key long term challenge. The understanding of thin films of p-wave superfluids ultimately benefits manufacturers of future devices of novel functionality based on new materials (eg unconventional superconductors). The development of cryogenic instrumentation and novel state-of-the-art measurement systems directly benefits the scientific instruments industry and users, including cryogenics and superconducting technologies industries, National Measurement Institutes, medical diagnostics.
Our expertise allows us to contribute advice to international funding agencies and scientific academies, and to engage with national laboratories. The embedded collaboration between the UK, mainland Europe and USA groups, and the links to Japanese groups significantly widens the communities who will benefit. The general public, including young people, is potentially excited and motivated such research.
How will they benefit?
Superfluid helium-three provides a test-bed for evolving theories of topological quantum matter. International networking with theorists, enhanced by the Hubbard Theory Consortium, ensures that ideas developed in helium physics propagate, influencing the materials discovery agenda as well as guiding the development of novel devices based in topological quantum matter and p-wave superconductors. The universality of the topological classification of condensed matter systems is new and exciting, and adds significantly to the established notions of new phases classified by their broken symmetries. Advances in fundamental understanding enter the canon of the subject, contribute to scientific progress and enhance the quality of life through unanticipated channels.
Such research acts as a magnet for the best young talent. It combines techniques at the frontiers of nanofluidics, ultralow temperature physics, measurement techniques, and addresses key theoretical concepts. Our experimental work revolves around custom design of equipment and instrumentation, the mastery of design skills and construction techniques, developing high precision measurement techniques and associated data acquisition schemes, data analysis, modelling; it involves managing the interaction with theorists. The rigorous training of highly skilled manpower, and the transfer of their expertise, enhances our economic competitiveness.
The cryogenic industry will benefit by contributions to the development of new refrigerator products with enhanced capabilities. The development of quantum nanofluidics helps open up nanoscience to the ultra-low temperature frontier. Combining nanoscience with ultralow temperature technology challenges us to develop new experimental methods. Developments in the applications of superconducting devices to NMR, made through this research, will be further advanced by collaborations with end users and will lead to novel MRI modalities, new techniques for NMR spectroscopy and biodiagnostics. The wider public, including school children, will benefit through a portfolio of outreach activities.
What will be done to ensure that they benefit?
Collaboration arrangements include: an established network with scientific instruments industry (eg Oxford Instruments Nanoscience) and standards laboratories (NPL and PTB); membership of the European MicroKelvin Collaboration, with dedicated activities for interaction and knowledge exchange. Joint workshops will be held involving the EPSRC funded TOPNES programme. Export of trained manpower; exploitation of novel instrumentation through national knowledge exchange schemes, such as HEIF, and the people pipeline. Wider communication and engagement activities will centre on outreach activities organised through our physics outreach officer; international conference and workshop participation and organisation.