Heuristic bounds on superconductivity and how to exceed them

Abstract

What limits the value of the superconducting transition temperature ($T_c$) is a question of great fundamental and practical importance. Various heuristic upper bounds on $T_c$ have been proposed, expressed as fractions of the Fermi temperature, $T_F$, the zero-temperature superfluid stiffness, ${\rho }_s(0)$, or a characteristic Debye frequency, ${\omega }_0$. We show that while these bounds are physically motivated and are certainly useful in many relevant situations, none of them serve as a fundamental bound on $T_c$. To demonstrate this, we provide explicit models where $T_c/T_F$ (with an appropriately defined $T_F$), $T_c/{\rho }_s(0)$, and $T_c/{\omega }_0$ are unbounded.

arXiv comment6 pages, 3 figures + appendices; (v2) Includes additional discussion, references and a revised title

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• Upper bounds on superconducting and excitonic phase-stiffness for interacting isolated narrow bands
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