Un-particle superconductivity in low-dimensional materials

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The phenomenon of superconductivity was discovered over a century ago. Over the course of the 20th century, researchers began to unearth its myriad of remarkable properties, including loss-less, high power electrical transmission, magnetic levitation and Josephson tunneling (used to determine fundamental constants with exquisite accuracy). In the 21st century, superconductivity is widely recognised as a pivotal player in the frontier development of quantum computation. On the theoretical side, the definitive theory of superconductivity was published by Nobel laureates John Bardeen, Leon Cooper and Bob Schrieffer over half a century ago. BCS theory proved to be remarkably successful, not only in explaining the properties of many known superconductors, but also in serving as a guide in the search for new superconductors, even those with an unconventional or anisotropic pairing symmetry. Over time, however, a number of superconducting materials have emerged that appear to challenge the BCS template. Significantly, their superconducting properties appear, in many respects, to be superior. Fundamental to BCS theory is the notion that Cooper pairing is an instability of a 'good' metal composed of coherent electronic states with long mean free path. Over the past few decades, however, superconductivity has also been discovered in 'bad' or 'strange metals', i.e. metals that do not conform to the standard models of metallic behaviour. Bad metals are characterized by an electron mean free path (at high temperatures) that diminishes to a fraction of the interatomic distance, while strange metals exhibit an electrical resistivity that grows linearly with temperature effectively from absolute zero right up to their melting point and a response in a magnetic field that follows an entirely different power law dependence to that seen in conventional metals.The core question now is whether BCS theory can account for the emergence of superconductivity in bad or strange metals or whether an entirely new paradigm is required. The fact that the electronic states in bad and/or strange metals lie at the coherent/incoherent boundary suggests that the condensation energy for superconductivity in these materials may derive from a saving in kinetic energy, rather than a saving in potential energy as is the case for BCS superconductors and that the superfluid condensate may emerge from the incoherent, rather than the coherent part of the electron self-energy. We call this alternative paradigm 'un-particle superconductivity'. The goal of this proposal is to explore the viability of un-particle superconductivity in candidate materials via a joint experimental/theoretical research programme that seeks to develop a theoretical framework for pairing of electronic states formed from the incoherent part of the electron spectral function and to test the resulting predictions with precise measurements of their superfluid density and carrier densities (both coherent and incoherent) in the normal, i.e. non-superconducting state. In total, three distinct material classes have been identified as candidate materials for the realization of un-particle superconductivity: copper-oxide high temperature superconductors, iron chalcogenides and one-dimensional purple bronze. Notably, superconductivity in the cuprates was discovered over 35 years ago, yet despite having been subject to the whole spectrum of experimental and theoretical techniques in condensed matter, smoking-gun evidence for BCS-type superconductivity remains elusive. Moreover, cuprates and iron chalcogenides are the only known materials to superconduct in monolayer form and at ambient pressures at temperatures above the boiling point of liquid nitrogen, making them highly attractive as platforms for future quantum computing devices. Finally, fulfillment of our research goals would lead to a new paradigm for (high temperature) superconductivity, one far-removed from the original BCS template.