Speaker: Tamaghna Hazra(Karlsruhe Institute of Technology)

Host: Rebecca Flint

Title: Not-so-high-Tc superconductivity: Upper bounds on the phase stiffness and superconducting critical temperature in two dimensional systems

Abstract: Magnets drive much of the world around us today. The most powerful ones are invariably superconducting electromagnets at very low temperatures which sustain tremendous currents without dissipation. A natural challenge for materials research is thus to identify ways and means to enable superconductivity at higher and more accessible temperatures, a quest that despite our best efforts over many decades has not yielded an ambient-pressure, room-temperature superconductor. 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.

Biography: Tamaghna is an Alexander von Humboldt research fellow at Karlsruhe Institute of Technology in Germany, working with Joerg Schmalian. During his PhD, he worked with Mohit Randeria at Ohio State University on the interplay of topology and strong correlations in superconductivity. As a postdoc, he worked with Piers Coleman at Rutgers University, exploring the interface of magnetism and superconductivity in heavy fermion systems. He then secured funding for independent research applying heavy fermion pairing mechanisms to moire systems, returning to the group of Joerg Schmalian at Karlsruhe where he had first started his journey in superconductivity research as an undergraduate intern. He likes distilling exact results that anchor intuition in simple models and seeking general organizing principles. He also enjoys working closely with experimental data, bridging theoretical models of exotic physics with sharp experimental signatures.