Singularity of the London penetration depth at quantum critical points in superconductors

TL;DR

This paper develops a comprehensive theory describing how the London penetration depth diverges at various quantum critical points within superconductors, with implications for experimental observations in iron-based materials.

Contribution

It introduces a universal framework for understanding the singular behavior of the London penetration depth at different quantum critical points in superconductors, including symmetry-breaking and topological transitions.

Findings

Universal critical exponents and amplitude ratios are identified.

Sign of the singularity depends on the interplay between critical theory and Fermi surface.

Application to experimental data in BaFe₂(As₁₋ₓPₓ)₂ shows relevance.

Abstract

We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents, and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with $\mathbb{Z}_2$ fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ (Hashimoto et al., Science 336, 1554 (2012)).