Enhancement of critical current density and mechanism of vortex pinning in H$^+$-irradiated FeSe single crystal

In this report, we comprehensively study the effect of H$^+$ irradiation on the critical current density, $J_c$, and vortex pinning in FeSe single crystal. It is found that the value of $J_c$ for FeSe is enhanced more than twice after 3-MeV H$^+$ irradiation. The scaling analyses of the vortex pinning force based on the Dew-Hughes model reveal that the H$^+$ irradiation successfully introduce point pinning centers into the crystal. We also find that the vortex creep rates are strongly suppressed after irradiation. Detailed analyses of the critical current dependent pinning energy based on the collective creep theory and extend Maleys method show that the H$^+$ irradiation enhances the value of $J_c$ before the flux creep, and also reduces the size of flux bundle, which will further reduce the field dependence of $J_c$ due to vortex motion.