 resistivity and magnetic susceptibility measurements under external pressure were performed on nafe underscore 1 underscore xco underscore x as single crystals with different doping levels x equals 0 0.01 0.028 0.075 and 0.109 the maximum t underscore c reached as high as 31 k under certain pressures for both underdoped and optimally doped samples meanwhile the over doped sample with x equals 0.075 also exhibits a positive pressure effect on t underscore c achieving an enhancement of 13 k under a pressure of 2.3 gpa all superconducting samples show large positive pressure coefficients on superconductivity while heavily over doped non superconducting nafe underscore 0.891 co underscore 0.109 as cannot be induced by pressure these studies reveal that the electronic structure is very different between superconducting and heavily over doped non superconducting nafe underscore 1 underscore xco underscore x as consistent with angle resolved photo emission spectroscopy observations this article was authored by a f Wang z j j yong j j ying and others we are article dot tv links in the description below