Doping evolution of the absolute value of the London penetration depth and superfluid density in single crystals of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$

The zero-temperature value of the in-plane London penetration depth, ${\lambda }_{ab}\left(0\right)$, has been measured in single crystals of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as a function of the Co concentration, $x$, across both the underdoped and overdoped superconducting regions of the phase diagram. For $x\gtrsim 0.047$, ${\lambda }_{ab}\left(0\right)$ has been found to have values between $120\pm 50$ and $300\pm 50\text{nm}$. A pronounced increase in ${\lambda }_{ab}\left(0\right)$, to a value as high as $950\pm 50\text{nm}$, has been observed for $x\lesssim 0.047$, corresponding to the region of the phase diagram where the itinerant antiferromagnetic and superconducting phases coexist and compete. Direct determination of the doping-dependent ${\lambda }_{ab}\left(0\right)$ has allowed us to track the evolution of the temperature-dependent superfluid density, from which we infer the development of a pronounced superconducting gap anisotropy at the edges of the superconducting dome.

Figure 1

Scanning electron microscope images of the Al-coated samples. (a) Large scale view. The broken side is on top. (b) and (c) are zoomed in on the Al film on the edge of the broken side. (d) A trench produced by a FIB. (e) Closeup view of the FIB trench showing the Al film and its thickness.

Figure 2

(Color online) Main frame: full superconducting transition of an optimally doped $\text{Ba}{\left({\text{Fe}}_{0.93}{\text{Co}}_{0.07}\right)}_2{\text{As}}_2$ crystal before and after coating. Inset: zoomed in low-temperature region, $T_{\text{min}}\lesssim T\lesssim T_c^{\text{Al}}$, before (green triangles) and after (red circles) the Al coating on the same sample. The overall frequency shift through the Al transition, denoted as $L$, is used for the calculation of ${\lambda }_{ab}\left(0\right)$.

Figure 3

(Color online) Top panel: the zero-temperature London penetration depth, ${\lambda }_{ab}\left(0\right)$, as a function of the Co concentration, $x$. The three dashed blue lines are theoretical curves obtained using Eq. (2) for three different values of ${\lambda }_{ab}\left(0\right)$ in the pure superconducting state. The solid gray line is a fit to the TDR data only of the form $A+B/x^n$. Also shown are values of ${\lambda }_{ab}\left(0\right)$ obtained by other experiments for comparison explained in the text. Bottom panel: phase diagram for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ (Refs. 2, 3, 9, 29).

Figure 4

(Color online) Top panel: ${\lambda }_{ab}^{-2}\left(T\right)$ for samples representing different doping regimes constructed using determined values of ${\lambda }_{ab}\left(0\right)$. Bottom panel: normalized superfluid density, ${\rho }_s\left(T\right)$, for the same samples shown in the top panel along with the standard $s$-wave and $d$-wave cases.