Speaker
Description
Understanding the material constraints that limit the critical temperature (Tc) is therefore pertinent to applied materials research, as well as our fundamental understanding of this remarkable phase of matter. In many strongly correlated materials, where estimating Tc is notoriously hard, we can place stringent constraints on the maximum possible Tc. I will present rigorous upper bounds on Tc in terms of the optical conductivity sum-rule, which is easier to measure experimentally and estimate theoretically. These constraints follow from exact upper bounds on the superfluid stiffness, an experimental measure of the rigidity of the U(1) phase that defines a superconductor. I will demonstrate the utility of these bounds for three strongly correlated materials of current interest. In a broad class of materials with flat bands, the low frequency optical conductivity may be dominated by a quantum geometric contribution - an inherently multi-band effect of non-trivial rotations in the Hilbert space of Bloch eigenfunctions in response to a vector potential. For these systems, I will present tighter bounds on the stiffness and 2D Tc in terms of the minimal spatial extent of the flat band eigenfunctions – demonstrating a deep connection between low energy optical conductivity and the Hilbert space geometry of multi-band Bloch Hamiltonians. Appreciating the limits on Tc in the presence of strong correlations helps us not only to benchmark materials in terms of their potential for higher Tc but also leads to qualitative insights guiding the search for strongly correlated materials where the maximum Tc is higher.
