Pressure effect on superconductivity of $A_{x}$Fe$_2$Se$_2$ ($A$ = K and Cs)

We performed the high hydrostatic pressure resistivity measurements (up to 1.7 GPa) on the newly discovered superconductors $A_{x}$Fe$_2$Se$_2$ ($A$ = K and Cs) single crystals. Two batches of single crystals $K_xFe_2Se_2$ with different transition temperatures ($T_c$) were used to study the effect of pressure. The $T_c$ of the first one gradually decreases with increasing pressure from 32.6 K at ambient pressure. While a dome-like behavior was observed for the crystal with $T_c=31.1$ K, and $T_c$ reaches its maximum value of 32.7 K at the pressure of 0.48 GPa. It indicates that there exists a optimal doping with maximum $T_c$ of 32.7K in $K_xFe_2Se_2$ system. The behavior of $T_c$ vs. pressure for $Cs_xFe_2Se_2$ also shows a dome-like behavior, and $T_c$ reaches its maximum value of 31.1 K at the pressure of 0.82 GPa. The hump observed in temperature dependence of resistivity for all the samples tends to shift to high temperature with increasing pressure. The resistivity hump could arise from the vacancy of Fe or Se.