Resistivity and magnetic susceptibility measurements under external pressure were performed on single-crystals NaFe1-xCoxAs (x=0, 0.01, 0.028, 0.075, 0.109). The maximum Tc enhanced by pressure in both underdoped and optimally doped NaFe1-xCoxAs is the same, as high as 31 K. The overdoped sample with x = 0.075 also shows a positive pressure effect on Tc, and an enhancement of Tc by 13 K is achieved under pressure of 2.3 GPa. All the superconducting samples show large positive pressure coefficient on superconductivity, being different from Ba(Fe1-xCox)2As2. However, the superconductivity cannot be induced by pressure in heavily overdoped non-superconducting NaFe0.891Co0.109As. These results provide evidence for that the electronic structure is much different between superconducting and heavily overdoped non-superconducting NaFe1-xCoxAs, being consistent with the observation by angle-resolved photoemission spectroscopy.
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