Superconductivity and non-Fermi liquid behavior near antiferromagnetic quantum critical points in CeRh$_{1-x}$Co$_x$In$_5$

Single crystals of CeRh$_{1-x}$Co$_x$In$_5$ have been investigated via measurements of specific heat, $C(x,T)$, and electrical resistivity under hydrostatic pressure, $\rho(x,P,T)$, up to $28$ kbar. Specific heat measurements for samples with cobalt concentrations of $x = 0.65, 0.71, 0.77, 0.87,$ and $0.93$ confirm the existence of antiferromagnetism (AFM) for $0\leq x \leq0.7$ and suggest the existence of a quantum critical point (QCP) at $x_c \sim 0.8$. Entropy vs $x$ isotherms below $\sim 5$ K and the normalized residual resistivity $\rho(0$ K$ )/\rho(290$ K) vs $x$ curve both display maxima near $x_c \sim 0.8$, suggesting further evidence for the existence and location of the QCP. Electrical resistivity measurements under pressure for samples with $x = 0.1, 0.2, 0.4$, and $0.6$ reveal AFM, pressure-induced superconductivity (SC), and the coexistence of AFM and SC. The $\rho(0$ K$ )/\rho(290$ K) vs $P$ curves favor the existence of QCP's at critical pressures $P_c \sim 24$ kbar for the $x = 0.1$, and $0.2$ samples and $P_c \sim 6$ kbar for the $x = 0.4$ sample. This research was supported by the U.S. DOE, NSF, and NNSA under the SSAA program.