Uploaded May 2024 | Updated September 2026, 2 weeks ago
Speaker: Joshuah T. Heath (Dartmouth College, New Hampshire)
Abstract: High-temperature superconductors are characterized by exotic normal states, and are still a subject of intense study nearly four decades after their introduction. A formal attempt to uniquely determine high-Tc behavior is given by Homes law: namely, that there is a linear relationship between T=0 superconducting ground-state properties and the T=Tc normal-phase DC conductivity. Homes law has been shown to work in the conventional (i.e., BCS) dirty limit, and remains a mostly empirical relation with an ill-defined origin. In this talk, I will outline theoretical and numerical work done on universal scaling relations in the context of electron-phonon superconductors described by Eliashberg theory. We find that Homes scaling is independent of both a high-Tc pairing mechanism and dirty BCS-like physics, and is instead a consequence of a non-Galilean invariant interaction. In the asymptotically strong limit, the Eliashberg equations reduce to a universal theory described by an Einstein spectrum, in which case we can make universal statements about scaling relations and the electromagnetic properties of strongly coupled electron-phonon superconductors. In this way, Homes scaling is shown to be a fundamental result in a wide class of superconducting compounds, and challenges the colloquial definition of “conventional” superconductivity.
Speaker: Joshuah T. Heath (Dartmouth College, New Hampshire)
Abstract: High-temperature superconductors are characterized by exotic normal states, and are still a subject of intense study nearly four decades after their introduction. A formal attempt to uniquely determine high-Tc behavior is given by Homes law: namely, that there is a linear relationship between T=0 superconducting ground-state properties and the T=Tc normal-phase DC conductivity. Homes law has been shown to work in the conventional (i.e., BCS) dirty limit, and remains a mostly empirical relation with an ill-defined origin. In this talk, I will outline theoretical and numerical work done on universal scaling relations in the context of electron-phonon superconductors described by Eliashberg theory. We find that Homes scaling is independent of both a high-Tc pairing mechanism and dirty BCS-like physics, and is instead a consequence of a non-Galilean invariant interaction. In the asymptotically strong limit, the Eliashberg equations reduce to a universal theory described by an Einstein spectrum, in which case we can make universal statements about scaling relations and the electromagnetic properties of strongly coupled electron-phonon superconductors. In this way, Homes scaling is shown to be a fundamental result in a wide class of superconducting compounds, and challenges the colloquial definition of “conventional” superconductivity.
