CP phase from Higgs's boundary condition

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We propose a new mechanism to generate a CP phase originating from a non-trivial Higgs vacuum expectation value in an extra dimension. A twisted boundary condition for the Higgs doublet can produce an extra dimensional coordinate-dependent vacuum expectation value containing a CP phase degree of freedom. With this mechanism, we construct a phenomenological model on S¹ which can simultaneously and naturally explain the origins of the fermion generations, the quark mass hierarchy and the structure of the Cabibbo-Kobayashi-Maskawa matrix with the CP phase.