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We study dynamics of a two-dimensional s-wave superconductor in the presenceof a moving single vortex. Our analysis is based on the quasiclassical theoryincluding the Hall term, generalized by Kita[T. Kita, PRB, 64, 054503 (2001)].We numerically calculate the linear response of a moving single vortex drivenby a dc external current in a self-consistent way, in the sense that Dysonequation, gap equation, Maxwell equations and generalized quasiclassicalequation are solved simultaneously. We obtain Hall conductivity induced byvortex motion using the generalized quasiclassical equation, while we confirmthat it vanishes in the conventional quasiclassical equation.

DC conductivity in an s-wave superconducting single vortex system