Quantum Phase Transitions and Quantum Criticality in Helium Films

Historically quantum fluids, the helium liquids near absolute zero, have provided simple model systems which have played a crucial role in the development of key concepts in condensed matter physics. The understanding of superfluidity and broken gauge symmetry; the development of the standard model of correlated fermions; the first unconventional superfluid/superconductor; the central role of topological excitations in two dimensional physics: all these discoveries and insights arose from the study of helium. The study of quantum fluids has also fuelled developments in techniques for producing and measuring low temperatures, high magnetic fields, and a host of novel measurement techniques and instrumentation. We propose to study a variety of low dimensional helium model systems to address fundamental issues in the understanding of strongly correlated quantum matter. We will study helium-3 (fermion) films and helium-4 (boson) films. These films grow as atomic layers on the atomically flat surface of graphite, and the lattice potential experienced by a helium layer can give rise to a triangular superlattice structure. The density of these layers can be varied essentially continuously to tune between different quantum mechanical ground states. These may include ground states theoretically proposed but yet to be unambiguously realized. We will study the quantum phase transitions between different ground states in some detail. We will study the Mott transition between a 2D helium-3 Fermi liquid and a 2D quantum spin liquid and the properties of the hole-doped spin liquid on a triangular lattice. We will attempt to stabilise a Mott insulator on a square lattice and perform a comparable experiment. In the corresponding helium-4 film we will study the superfluid-insulator transition, and investigate possible 2D supersolid behaviour. We will develop a highly ordered graphite substrate with a view to optimising conditions under which to search for the holy grail of unconventional superfluidity in a helium-3 fluid monolayer. We will investigate quantum criticality in the helium-3 bilayer heavy fermion system recently discovered by us. And we will study helium-3 in nano-channels as a one dimensional fermion system, and a possible realization of a Luttinger liquid. These experiments on fermionic and bosonic cold atoms are performed on uniform low dimensional systems in thermodynamic equilibrium at precisely measured temperatures in the range 200 microKelvin to 4K. The lowest temperatures will be produced by nuclear adiabatic demagnetization cryostats in our laboratory. A range of high precision experimental probes will be employed to study these systems. Sensitive NMR techniques developed in our laboratory, based on the detection of the precessing magnetic signal by SQUIDs (Superconducting Quantum Interference Devices), will be used to measure magnetic susceptibility, magnetization and spin dynamics. We will extend measurements of the heat capacity to the lowest temperatures in order to access system entropy and probe the elementary excitations. The superfluid density, and any dissipative component of the response, will be measured by high quality torsional mechanical resonators. We will collaborate on developing graphene based nano-mechanical resonators with wide-bandwidth SQUID amplifier detection. The project is expected to lead to fundamental insights into some of the most central issues in the physics of strongly correlated matter, and impact on the understanding of more complex materials of potential technological relevance. The project will drive innovation of new instrumentation and measurement techniques at an important scientific frontier; the low temperature frontier. As in any frontier science we may encounter the unexpected.

Who will benefit? The research proposed here exploits helium to confront fundamental issues of wide significance and relevance in condensed matter physics. It underpins work on technologically relevant materials. It ultimately benefits manufacturers of new devices of novel functionality based on new materials, their users and society. In addition, the proposed research involves the development of cryogenic instrumentation and novel measurement systems involving the use of state-of-the-art superconducting devices as amplifiers. It directly benefits the scientific instruments industry and users of such instrumentation, including cryogenics industry, superconducting technologies industry, medical imaging and diagnostics. Expertise in this frontier area of research allows us to contribute advice nationally and internationally, mostly to funding agencies and scientific academies, and to engage with national laboratories. The wider public is potentially excited by advances in low temperature physics, a visual subject, and a playground for demonstrating exotic quantum phenomena. How will they benefit? The simplicity of helium provides a test-bed for the new and evolving theories of strongly correlated condensed matter, and the effects of low dimensionality. Strong networking with theorists, enhanced by the establishment of a new theory of condensed matter activity, will ensure that ideas developed in helium physics propagate, to influence the materials discovery agenda. Advances in fundamental understanding enter the canon of the subject, contribute to scientific progress and enhance the quality of life through unanticipated channels. Our understanding of condensed matter is at a crossroads; it is hard to predict the timescale on which the paradigm shift will occur. The highest quality fundamental research acts as a magnet for the best students and young talent. A key impact of our research is the rigorous training of highly skilled manpower. 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 training of such manpower enhances our economic competitiveness. The cryogenic industry will benefit by contributions to the development of new refrigerator products, or products with enhanced capabilities. Our expertise will provide necessary credible thermometry for the mK temperature range. Developments in the applications of superconducting devices to NMR, made through this research, will be further advanced by scientific collaborations with end users. Our fundamental research will continue to be the driver for improving sensitivity and technique. The major benefit will be novel MRI modalities, based around compact systems, new techniques for NMR spectroscopy and biodiagnostics. New developments in nano-mechanical resonators are also planned. The wider public, including school children, will benefit through a portfolio of outreach activities designed to encourage interest in science and to promote scientific endeavour and its societal benefits. What will be done to ensure that they benefit? Collaboration arrangements include: an established network of strong collaborations with scientific instruments industry and standards laboratories; an enhanced European network through membership of the European MicroKelvin Collaboration, funded by FP7, with dedicated activities for interaction and knowledge exchange 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 dedicated physics outreach officer; international conference and workshop participation and organisation.