Superconductivity and Quantum Criticality in $\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}{\mathrm{n}}_{\mathrm{5}}$

Electrical resistivity measurements on a single crystal of the heavy-fermion superconductor $\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}{\mathrm{n}}_{\mathrm{5}}$ at pressures to 4.2 GPa reveal a strong crossover in transport properties near $P^{*}\approx 1.6\mathrm{G}\mathrm{P}\mathrm{a}$, where $T_c$ is a maximum. The temperature-pressure phase diagram constructed from these data provides a natural connection to cuprate physics, including the possible existence of a pseudogap.

Figure 1

Effect of pressure on the low-temperature resistivity and superconducting $T_c$ of $\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}{\mathrm{n}}_{\mathrm{5}}$. The inset shows the resistivity $\rho$ normalized by $\rho (T_c^{+})$ up to 10 K.

Figure 2

Representative plots of $[\rho (T)-{\rho }_0]/T^n$ vs $T$. At low pressures, $[\rho (T)-{\rho }_0]/T^n$ is constant from $T_{pg}\approx (1.15\pm 0.05)T_c$ to about 10 K. At the higher pressures, there is a well-defined range below $T_{\mathrm{F}\mathrm{L}}$ where $(\rho -{\rho }_0)\propto T^2$ is Fermi-liquid-like. The resistive onset of superconductivity, defined by the intersection of linear extrapolations of $\rho (T)$ from above and below $T_c$, is denoted by dashed vertical arrows. At the highest pressures, the gradual rounding just above $T_c$ is due to a broadened transition (see Fig. 3) and not to $T_{pg}$.

Figure 3

(a) Values of ${\rho }_0$ and $n$ obtained from plots as shown in Fig. 2. (b) Temperature coefficient of resistivity, $A$, associated with values of $n$ given in the top panel, and specific heat coefficient $\gamma$ measured directly ($P<1.5\mathrm{G}\mathrm{P}\mathrm{a}$) and, for $P>2\mathrm{G}\mathrm{P}\mathrm{a}$, inferred from the $T^2$ coefficient of $\rho (T)$. See text for details. (c) Superconducting transition width normalized by $T_c$. $\Delta T_c$ and $T_c$ are the half-width of the resistive transition width and resistive midpoint, respectively. Solid lines in all cases are guides to the eye.

Figure 4

(a) Temperature-pressure phase diagram for $\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}{\mathrm{n}}_{\mathrm{5}}$ constructed from data shown in Figs. 2, 3 . (b) Schematic $T\mathrm{–}P$ phase diagram. AFM: Néel state; PG: pseudogap state; SC: unconventional superconducting state; FL: Fermi-liquid; NFL: non-Fermi-liquid. See text for details.