$c$-axis charge gap and its critical point in the heavily doped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

Abstract

Temperature-dependent inter-plane resistivity, ${\rho }_c(T)$, was used to characterise the normal state of the iron-arsenide superconductor Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ over a broad doping range $0\le x<0.50$. The data were compared with in-plane resistivity, ${\rho }_a(T)$, and magnetic susceptibility, $\chi (T)$, taken in $H\perp c$, as well as Co NMR Knight shift, ${}^{59}K$, and spin relaxation rate, $1/T_{1}T$. The inter-plane resistivity data show a clear correlation with the NMR Knight shift, assigned to the formation of the pseudo-gap. Evolution of ${\rho }_c(T)$ with doping reveals two characteristic energy scales. The temperature of the cross-over from non-metallic, increasing on cooling, behavior of ${\rho }_c(T)$ at high-temperatures to metallic behavior at low temperatures, $T^{\ast }$, correlates well with an anomaly in all three magnetic measurements. This characteristic temperature, equal to approximately 200~K in the parent compound, $x$=0, decreases with doping and vanishes near $x^{\ast }\approx$0.25. For doping levels $x\ge 0.166$, an additional feature appears above $T^{\ast }$, with metallic behavior of ${\rho }_c(T)$ found above the low-temperature resistivity increase. The characteristic temperature of this charge-gap formation, $T_{\mathrm{CG}}$, vanishes at $x_{\mathrm{CG}}\simeq$0.30, paving the way to metallic, $T$-linear, ${\rho }_c(T)$ close to $x_{\mathrm{CG}}$ and super-linear $T$-dependence for $x>x_{\mathrm{CG}}$. None of these features are evident in the in-plane resistivity ${\rho }_a(T)$. For doping levels $x<x_{\mathrm{CG}}$, $\chi (T)$ shows a known, anomalous, $T$-linear dependence, which disappears for $x>x_{\mathrm{CG}}$.

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