Heuristic bounds on superconductivity and how to exceed them

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.

Automated summary

This article discusses the limits of the superconducting transition temperature (T-c) based on various heuristic upper bounds. It shows that these bounds, although physically motivated and useful in many cases, do not serve as a fundamental limit for T-c.