Study on the non-bulk superconductivity in CaFe$_{2}$As$_{2}$ single crystals under different annealing conditions.

The interplay between SDW and tetragonal/collapsed tetragonal(T/cT) structural transition in CaFe$_{2}$As$_{2}$ single crystals under different annealing conditions has been thoroughly investigated, while the occurrence of filamentary superconductivity with T$_{c}$ $\sim$ 10K remains mysterious. In this talk, I will present our studies on the interplay of magnetism, structural transition, and superconductivity in the undoped CaFe$_{2}$As$_{2}$ single crystals obtained under different synthetic conditions and annealing procedures. The diamagnetic shift has been detected for the first time and taken as an evidence of superconductivity. High temperature annealing and low temperature annealing drive CaFe$_{2}$As$_{2}$ into the cT ground state and the T ground state, respectively. The superconductivity signal is maximized in the condition where the sample reaches the unstable region at the border of these two. The detailed results and their implications will be presented and discussed.