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While unusual normal state properties, such as non-Fermi liquid behavior ofthe resistivity, are commonly associated with strong quantum fluctuations,evidence for its presence inside the superconducting dome are much scarcer. Inthis paper, we use sensitive and minimally invasive optical magnetometry basedon NV-centers in diamond to probe the doping evolution of the $T=0$ penetrationdepth in the electron-doped iron-based superconductorBa(Fe$_{1-x}$Co$_x$)$_2$As$_2$. A non-monotonic evolution with a pronouncedpeak in the vicinity of the putative magnetic QPT is found. This behavior isreminiscent to that previously seen in isovalently-substitutedBaFe$_2$(As$_{1-x}$P$_x$)$_2$ compounds, despite the notable differencesbetween these two systems. Whereas the latter is a very clean system thatdisplays nodal superconductivity and a single simultaneous first-ordernematic-magnetic transition above, and even somewhat below, $T_c$, the formeris a significantly dirtier system with fully gapped superconductivity and splitsecond-order nematic and magnetic transition above $T_c$. Thus our observationthat such distinct systems display remarkably similar penetration depth peaks,combined with the theoretical result that a QPT alone does not ensure theexistence of a peak, unveils a puzzling and seemingly universal manifestationof quantum fluctuations in the iron pnictides.

new journal of physics

Quantum phase transition inside the superconducting dome of  Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ probed by optical magneto-sensing using  NV-centers in diamond