Frustration and reduced dimensionality as routes to new forms of quantum order

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When steam cools down, fast-moving water molecules condense into water. And if this water is cooled further, the watermolecules stop moving altogether, and organize themselves into the beautiful crystal structures we know as ice. All ofthe materials we use to make electronic devices --- for example the semi-conductor brain'' of the computer you arenow using - contain mobile electrons in a liquid or gas-like state. So what happens to these electrons when they cooldown ? The answer depends on the chemical structure of material in which they live.In some materials the electrons form a solid, rather like the water molecules in ice. Some become magnetic. And somebecome superconductors'' - a remarkable type of metal whose electrical resistivity is exactly zero. Such systemsare said to exhibit different forms of order'', which is to say that the electrons they contain organize themselvesin different ways when they are cooled down. One of the most important themes in 21st century materials science is thesearch for materials whose electrons exhibit completely new forms of order. This is a problem as fundamental as thesearch for new types of elementary particle. But it is also one of profound technological significance, since thesenew materials may one day be used to build new forms of electronic device.This proposal combines state-of-the-art theory and experiment, with the goal of exploring how new forms of quantumorder can arise in systems where no simple form of order wins outright, and the electrons are frustrated (muchlike people) by the bewildering array of choices which they face. The experimental systems we consider are at the forefront of modern materials science, and are unique in their physical behaviour. In LiV2O4, vanadium d-electrons become as massive as muons.In Na4Ir3O8, magnetic Ir ions fail to order magnetically at any temperature. PrBa2Cu4O8 is the most one-dimensional metal known to exist, whilst the organic compounds kappa-(ET)2Cu2(CN)3 and kappa-(ET)2Cu[N(CN)2]Cl, provide a long-sought realization of quantum spins on a highly-frustrated triangular lattice.Our main experimental approach will be to measure how these systems transport heat and electricity. The ratio of thermal and electrical conductivities, measured over a range of temperatures, is a very sensitive test of the way in which the electrons in a given material have organized themselves. Measuring this ratio will enable us to establish that these materials are completely unlike conventional metals and insulators. We will also study how their electronic characteristics, such as mass, evolve as the systems become more frustrated. At the same time, we will use super-computers to solve mathematical models of how unconventional order might work in these and materials. In particular we try to understand how electrons work together to form new types of elementary excitation'', for example particles with half the charge of an electron ! If successful, this work has the potential to change how we think about metals forever...