High temperature superconductors were discovered 32 years ago (1986), and there is still no consensus on the mechanism that makes them superconducting, other than it is not the Bardeen-Cooper-Schrieffer (BCS) electron-phonon mechanism generally believed to explain low temperature "conventional" superconductors. Several other families of superconducting materials have been discovered in the last 40 years that do not fit the BCS framework. The field is in stagnation, and I argue it will not make progress until it is recognized that low temperature "conventional" superconductors are misunderstood by BCS theory [1]. I will give an overview of analytic and computational work by our group over the last 30 years that aims to describe all superconducting materials within a unified framework, the theory of hole superconductivity [2], that naturally explains the Meissner effect, the most fundamental property of superconductors. The theory proposes that the driving mechanism for superconductivity is not electron-phonon interaction but lowering of quantum kinetic energy, and that only carriers at the top of electronic energy bands (holes) can give rise to superconductivity. I will discuss computational work on dynamic Hubbard models that describe this physics. The theory explains why in superconducting elements the Hall coefficient is positive and why in high temperature superconductors the critical temperature is high, and provides guidelines in the search for higher temperature superconductors. I will discuss the many open questions and opportunities for future research in this field along these lines.

[1] J. E. Hirsch, "BCS theory of superconductivity: it is time to question its validity", Physica Scripta 80, 035702 (2009).
[2] References in https://jorge.physics.ucsd.edu/hole.html

Jorge E. Hirsch is an Argentine American professor of physics at the University of California, San Diego. He is known for inventing the h-index in 2005, an index for quantifying a scientist's publication productivity and the basis of several scholar indices.

Hirsch was born in Buenos Aires, Argentina. He earned an undergraduate degree at the University of Buenos Aires, received his PhD from the University of Chicago in 1980 and served as a post-doctoral research associate in the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. Following this experience, he joined the University of California, San Diego Department of Physics in 1983.

Hirsch's scientific work is involved with understanding collective, large-scale properties of solids, such as superconductivity and ferromagnetism, based on explanations starting from small-scale mechanisms. He has published 248 papers that have received 16,380 citations. Hirsch's most significant work would be his attempt to unify theories of superconductivity with his theory of hole superconductivity which suggests pairing of holes that would lead to superconductivity in all materials, as opposed to pairing of electrons in conventional BCS theory.