Origin of critical temperature universal scaling relations in type-II superconductors

Abstract

Understanding the intricate relationship amongst fundamental properties of superconductors, in general, is paramount for unraveling the origin of high-temperature superconductivity. An analytical formula for the superconducting transition temperature Tc is derived from the T→0 limit of a recently proposed expression for the vortex glass melting line, Hg(T), wherein the energy scale kBTc is shown to be proportional to the product of the ground state condensation energy density Hc2∕2μ0, a Cooper pair coherence volume Vcoh, and the Lindemann number cL, which characterizes the stability of the solid vortex state to thermal and quantum fluctuations. This expression provides a fundamental starting point from which the empirical scaling relation ρs∝σdcTc, established by Homes et al. [Nature (London) 430, 539 (2004)], as well as other recent observations, can be derived. Compatibility of the “bad metal” theory of superconductivity of Emery and Kivelson [Nature (London) 374, 434 (1995)] with the results obtained herein is examined.

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