Dependence of Superconducting Transition Temperature on Uniaxial Pressure in CeCoIn$_5$

We apply uniaxial pressure up to 4 kbar along the $c$-axis of single crystal samples of CeCoIn$_5$ and measure how the transition temperature to the superconducting state changes. We mount the sample within an ac susceptibility coil and apply pressure through a helium bellows cell mounted on a dilution refrigerator. We find that pressure shifts the transition to lower temperatures at a rate of 22.5 mK per kbar. Our observation follows the general correlation between transition temperatures and lattice constants among 115 materials, where lower $T_c$'s typically correspond to smaller $c/a$ ratios. Pressure has the additional effect of broadening the transition well beyond what we expect from macroscopic pressure inhomogeneity. We are extending this work to measurements of CeCoIn$_5$ under $a$-axis pressure.