Heuristic bounds on superconductivity and how to exceed them

TL;DR

This paper challenges existing heuristic bounds on the superconducting transition temperature ($T_c$), demonstrating through models that these bounds are not fundamental limits and can be exceeded.

Contribution

The authors show that proposed heuristic bounds on $T_c$ based on $T_F$, $ ho_s(0)$, and $\omega_0$ are not fundamental, providing explicit models where these ratios are unbounded.

Findings

Heuristic bounds on $T_c$ are not fundamental.

Explicit models demonstrate unbounded $T_c$ ratios.

Existing bounds can be exceeded in certain models.

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.