Abstract

I will examine how new exotic electronic states emerge in pure materials around quantum critical points. Such points are found when a continuous phase transition between apparently simpler states takes place at zero temperature. In practice continuous phase transitions almost always become discontinuous (first-order) as their transition temperatures are suppressed towards zero kelvin by varying a single parameter, such as pressure. Several independent parameters therefore have to be tuned together to bring a material exactly to a quantum critical point. The strong magnetic anisotropy of URhGe allows such multiple-parameter magnetic-tuning to be realised in practice. Remarkably, around the quantum critical point an unusual form of superconductivity occurs in which parallel-spin electrons become paired, in contrast with anti-parallel spin-pairing found in almost all other superconductors. More remarkably still, although the superconductivity only forms below 0.5 kelvin, it can survive in magnetic fields of over 28 tesla as the quantum critical point is moved to increasing field by tilting the field direction away from the easy magnetic plane. This provides one of the most dramatic examples of a growing number of new electronic states of matter formed close to quantum critical points with very novel properties.