Macroscopic and microscopic physical properties of Fe
1+δSe
xTe
1-x were investigated through the magnetic susceptibility, electrical resistivity, heat capacity and nuclear magnetic resonance (NMR) measurements. The mother compound Fe
1.14Te shows an antiferromagnetic phase transition accompanied by the structural change at 61.5K. The antiferromagnetic transition temperature of Fe
1+δSe
xTe
1-x decreases with increasing
x, then the superconducting transition appears above
x = 0.2. The superconductivity with clean limit occurs when δ is small. In such a compound, the temperature dependence of the nuclear spin - lattice relaxation rate and the electron contributed specific heat reveals presence of the nodal superconducting gap structure, suggesting that the superconductivity occurs in an unconventional mechanism. From a systematic investigation of the nuclear spin - lattice relaxation rate in Fe
1+δSe
xTe
1-x, it was found that the antiferromagnetic quantum critical point lies at
x ∼0.03. The superconductivity occurs in the vicinity of the antiferromagnetic quantum critical point, resulting in that the superconductivity in Fe
1+δSe
xTe
1-x is mediated by the antiferromagnetic spin fluctuations.
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