Fluctuation Induced Exotic Phases of Quantum Matter

Usually fluctuations have a destabilising effect. When carrying a tray of drinks through a crowded room one wishes to avoid the jostling of the crowd. Similarly, a tightrope walker would probably avoid performing on a blustery day.

However, there are many instances where fluctuations can have the opposite effect, stabilising a system in a configuration that might otherwise be unstable. This occurs when the noise is state-dependent; that is, when the spectrum of the fluctuating forces experienced by the system is modified by the particular configuration of the system. Examples include the balancing of a broom on ones fingertip - practice leads the expert to approach ever more closely to a Levy flight distribution of horizontal movements. The crucial point is that the torque experienced by the broom depends upon its angle to the vertical. Many other examples may be viewed in this way. For example, adaptable species, agile businesses and diverse investment strategies are all stable because of fluctuations in the environment.

This phenomenon can also occur in quantum systems. In this case, the fluctuations concerned are intrinsic quantum fluctuations occurring because of Heisenberg's uncertainty principle. A quantum oscillator must always oscillate a little because of the uncertainty principle and so always carries a little energy, known as the zero-point energy. Changing the state of the system can change the frequency of these intrinsic quantum oscillations and so change the zero point energy. When the quantum fluctuations are very strong, reducing the zero point energy can be the main influence deciding the state that the system adopts.

Applying this idea to metals with very strong quantum fluctuations has proven very useful in understanding novel states observed in experiment. Indeed, the observation of novel states has driven developments of aspects of the theory and the perspective suggested by the theory has suggested experiments. This proposal will continue to develop this approach - which has become known as fermionic quantum order-by-disorder. We aim to make progress in four key directions:

- Extend the theoretical approach to new systems
- Extend the accuracy of the theoretical approach
- Explore novel quantum order experimentally
- Experimental and Theoretical discovery

Showcase UK Science: The ideas of fermionic quantum order by disorder that underpin this grant application have been very successful with 3 Physical Review Letters, 1 Physical Review B Rapid Communication, 2 Physical Review B regular articles and a Nature Physics Letter over the past couple of years. Much of this work has been focused upon explaining experimental results found in research teams outside of the UK. A deliberate effort to press these ideas forward in concert with experiment will provide a showcase for UK materials science as a driver of experiment and ideas - as demonstrated by the Nature Physics Letter, which was produced by the team involved in this proposal.

Technology: This research proposal is focused upon basic materials science. However, the discovery of new materials underpins technological progress.
New electronic properties are particularly useful in the information age. Enriched understanding of the thermodynamic properties of materials in the vicinity of phase transitions will play an important role in the search for more efficient ways to store and transmit energy. The main technological impact of this programme will be in the search for materials with such useful bulk properties. A certain amount of serendipity is required for this type of discovery. By deliberately fostering interaction between analytical, numerical and experimental efforts - as well as developing an intuitive, physically motivated perspective - we aim to enhance the frequency of such discovery and our ability to take advantage. The timescales to harness new material properties can be surprisingly short [as illustrated by incorporation of materials displaying Giant Magneto Resistance in information storage devices]. This proposal describes a programme of basic science, positioned and structured in such a way that it can feed rapidly into technological advance when opportunity arises.

Materials Modelling: It seems likely that the ideas of quantum order-by-disorder might be incorporated into density functional theory. We propose a pilot study at an early stage in our programme to investigate this possibility. The UK materials modelling community has pioneered many innovative uses of density functional theory and written and commercialised some of the most successful and widely-used code. We will work with some key players in this area during our pilot study, giving the best chances for rapid development and release of commercially useful insights.

Capacity: A central benefit of this proposal is the human/scientific capacity that it will develop. Interdisciplinary work succeeds by engaging specialists from different areas with a common goal. As well as developing the specialist skills of PhDs and post-doctoral research associates, by fostering close engagement from the outset, this programme will equip them with the common lexicon that is required for interdisciplinary research. We believe that this will be crucially important in addressing the scientific and technological challenges that the world now faces.