DFT+mu: a step change in muon spectroscopy

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Muon spectroscopy is a powerful experimental technique in condensed matter physics. It involves using the muon, a subatomic particle, as a microscopic magnetometer that we implant into matter, in order to probe the local environment. Use of the muon technique has led to a large number of key advances in our knowledge of quantum magnetism, unconventional superconductivity, semiconductor physics, charge transport and dynamical processes in solids. Despite its clear successes, questions about the validity of muon spectroscopy are still regularly raised, owing to our lack of knowledge of the site of the stopped muon in the solid and the influence that the charged muon probe has on its local environment. This is especially important in a number of high profile cases in which the muon measurements reveal effects that have not been observed with other techniques. In the last two years, we have shown that it is possible to accurately calculate the properties of muon stopping states using pioneering methods based on electronic structure calculations. Although our initial results are very promising, the techniques remain in their infancy and generally approximate the muon as a classical, rather than as a quantum mechanical, particle. We now propose to develop the methods, fostering a quantum mechanical approach, in order to address a range of important, current problems in condensed matter, including superconductivity, frustrated and low-dimensional magnetism and topological phases. Our results will not only dramatically improve a key experimental technique for studying advanced materials, but will directly contribute to research into new materials.