Superconducting Quantum Critical Point in ${\mathrm{CeCoIn}}_{5-x}{\mathrm{Sn}}_x$

We report a combined pressure-doping study in the nearly two-dimensional heavy fermion superconductor ${\mathrm{CeCoIn}}_5$ as its superconducting phase is driven to the normal state by Sn doping and/or applied pressure. Temperature-pressure-dependent electrical resistivity measurements were performed at the vicinity of a superconducting quantum critical point where $T_c\to 0$. A universal plot of the concentration- and pressure-dependent phase diagram suggests that for the concentrations studied a single mechanism is responsible for reducing $T_c$ and bringing the system to the superconducting quantum critical point. A two-band model with hybridization controlled by pressure and doping provides a consistent description of the phase diagram and the suppression of the $d$-wave superconductivity in this material.

Figure 1

The left panel shows the high-$T$ behavior of the electrical resistivity for ${\mathrm{CeCoIn}}_{5-x}{\mathrm{Sn}}_x$. The inset shows the temperatures of the maxima in the resistivity as a function of doping. The right panel presents selected low-$T$ electrical resistivity curves exhibiting the superconducting transitions.

Figure 2

The lower panel shows the ambient pressure-temperature-composition phase diagram for ${\mathrm{CeCoIn}}_{5-x}{\mathrm{Sn}}_x$. In the right extreme it is shown the pressure evolution of $T_{\mathrm{coh}}$ for ${\mathrm{CeCoIn}}_{4.82}{\mathrm{Sn}}_{0.18}$ (see the text). The upper left panel exhibits the sublinear $T^n$ behavior in a log-log plot just above the superconducting transition for several compositions. The upper right panel shows the linear behavior of the resistivity for ${\mathrm{CeCoIn}}_{4.82}{\mathrm{Sn}}_{0.18}$, which is at the critical concentration.

Figure 3

Pressure-dependent electrical resistivity curves as a function of temperature for ${\mathrm{CeCoIn}}_{4.90}{\mathrm{Sn}}_{0.10}$.

Figure 4

Pressure-temperature phase diagram for ${\mathrm{CeCoIn}}_{4.88}{\mathrm{Sn}}_{0.12}$. The inset shows normalized $\rho (T)$ for $P\ge 15\mathrm{kbar}$, evidencing the FL signature up to $\sim 1.2\mathrm{K}$.

Figure 5

$T_c$ versus $P$ phase diagrams via experimental data for different doping and theoretical lines results. $T_c(P)/T_c(P=0)$ versus $P/P_c$ phase diagram with a universal curve with normalized experimental data for different values of doping $x$. $T=0P_c(x)/P_c(x=0)$ versus $x$ phase diagram containing the theoretical prediction points for different doping and a linear fitting.