Are there bounds on the superconducting transition temperature?
Dr. Mohit Randeria
Ohio State University
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Faculty Host: Chris Hammel
Abstract: Understanding limits on the superconducting transition temperature Tc is a question of fundamental and practical importance. I will begin by describing developments in quantum materials and ultracold atoms that challenge conventional wisdom on what controls Tc. I will then describe exact upper bounds [1] on Tc for two dimensional (2D) systems, valid for any pairing mechanism or strength. The 2D bound takes a particularly simple form for parabolic dispersion -- Tc cannot exceed one-eighth the Fermi temperature – which has been realized in recent experiments [2,3]. I will next describe results for multi-band systems with complex band structures and discuss applications to 2D superconducting materials including twisted bilayer graphene. I will briefly describe progress on topological flat bands, where the Tc bound [4] involves the “quantum geometry” of electronic wave functions. I will conclude by describing the challenges in deriving bounds on Tc in 3D, which remains an open problem.
[1] T. Hazra, N. Verma, M. Randeria, Phys. Rev. X 9, 031049 (2019)
[2] Y. Nakagawa et al., Science 372, 190 (2021)
[3] M. Randeria, Science 372,132 (2021)
[4] N. Verma, T. Hazra, M. Randeria, Proc. Nat. Acad. Sci. 118, e2106744118 (2021)
