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Competition between superconductivity and disorder plays an essential role inunderstanding the metal-insulator transition. Based on the Bogoliubov-de Gennesequation, we studied an s-wave superconductor with both spin-orbit coupling anddisorder are presented. With increasing the strength of disorder, the meansuperconducting order parameter will vanish while the energy gap will persist,which indicates that the system undergoes a transition from a superconductingstate to an insulating state. This can be confirmed by calculating the inverseparticipation ratio. We also find that, if the strength of disorder is small,the superconducting order parameter and the energy gap will decrease if weincrease the strength of spin-orbit coupling and Zeeman field. In the largedisorder limits, increasing the strength of spin-orbit coupling will increasethe mean superconducting order parameter. This phenomenon shows that the systemis more insensitive to disorder if the spin-orbit coupling is presented.Numerical computing also shows that the whole system breaks up into severalsuperconducting islands instead of being superconductivity.

Anderson Localization in Degenerate Spin-Orbit Coupled Fermi Gases with Disorder