Unconventional superconductivity

Professor Mark van Schilfgaarde of King’s College London is an expert in the theory of electronic structure, the key to understanding properties of materials at their most fundamental level. He is particularly known for his work in Quasiparticle Self-Consistent GW theory (QSGW), a new formulation of one of the most advanced approaches to electronic structure – the GW approximation. QSGW dramatically improves the quality of GW and makes it suitable for studying a number of interesting materials.

A recent development of QSGW aimed to extend the theory to treat strongly correlated systems such as unconventional superconductors by combining it with dynamical mean-field theory (DMFT). DMFT is a non-perturbative theory that provides information about the short-range correlations between electrons that GW cannot. “As long as you are working with a strongly correlated system where all the interesting things happen within a few degrees of freedom – as is the case with unconventional superconductors like iron selenide and YBCO – DMFT is much more tractable than GW,” says van Schilfgaarde.

Around twenty years ago, researchers began using DMFT in conjunction with density functional theory to study materials, but by using GW instead of density functional theory, van Schilfgaarde has created a high-fidelity theory that can accurately describe unconventional superconductors and provide information about the structure of their Cooper pairs.

DMFT provides a way of partitioning the study of unconventional superconductors into two parts – a strongly correlated part and a weakly correlated part. The whole system is first calculated using QSGW, after which the strongly correlated sub-space is calculated using DMFT and embedded into the original calculation. The influence of this sub-space on the rest of the system is then calculated to make it self-consistent. This process is then repeated over and over until a quantity known as the Green’s function stops changing.

“Our theoretical developments have helped us make a lot of progress,” says van Schilfgaarde. “We are a long way from solving everything, but we can do things that we could not do before, like predicting the superconducting critical temperature and examining the way in which the superconducting state competes with other states like ferromagnetism.”

This theory has for the first time provided a method for studying the structure of Cooper pairs in unconventional superconductors without relying on density functional theory or on models. “A big problem in the field of superconductivity research is that it is so complicated that it almost entirely relies on models,” explains van Schilfgaarde. “This is not to denigrate the work of those who create these models – these people are brilliant physicists who have created intricate and ingenious theories for explaining superconductivity. However, the models all rely on assumptions that we have no basis for knowing whether they are correct or not, which has led to a lot of confusion in the literature and a lack of consensus about the mechanisms behind superconductivity.”