Many proposals have been suggested for achieving giant Kerr nonlinearity in different medium [1,2]. In this study we propose a new model for achieving giant Kerr nonlinearity in a single layer of graphene nanostructure. The properties of electron near the Dirac points make it possible for interacting by electromagnetical fields . The nonlinear optical features of graphene nanostructure in the presence of strong magnetic field have been discussed very recently in four-wave mixing . To the best of our knowledge, the giant Kerr nonlinearity of graphene with zero linear and nonlinear absorption has not been reported theoretically or experimentally. The enhanced Kerr nonlinearity with zero linear absorption is very interested in nonlinear optics and quantum information science.
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