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

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)).

(4+4) pages, 4 figures; (v2) minor changes, added supplementary material. To appear in Phys. Rev. Lett

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• Anomalous thermodynamic properties of quantum critical superconductors
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• Impact of ordering competition on the global phase diagram of iron pnictides
• Topological Defects in Systems with Two Competing Order Parameters: Application to Superconductors with Charge- and Spin-Density Waves
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• Cluster structure of superconducting phase and the nature of peaks in the doping dependences of the London penetration depth in iron pnictides
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• Incommensurate magnetic states induced by ordering competition in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}\mathrm{N}{\mathrm{a}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
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• Impurity bands in magnetic superconductors with spin density wave
• Quasiclassical theory of $C_4$-symmetric magnetic order in disordered multiband metals
• Absence of coherent peaks in a $Z_2$ fractionalized BCS superconducting state
• Magnetic Quantum Criticality inside the Superconducting State Revealed by Penetration Depth Scaling with Local $T_{\mathrm{c}}$