Self-resonant current steps of Josephson tunnel junctions in the presence of multimode oscillation

Taking into account the presence of multimode oscillation, self-resonant current steps in current-voltage characteristics of rectangular Josephson tunnel junctions are studied theoretically. An expression for the zero-field step is obtained, which is shown to be significantly different from previous theories assuming a single-mode oscillation. For a long junction with a length larger than the Josephson penetration depth, the present theory gives the magnetic field dependence of the Fiske step, whose shape is considerably changed from the one calculated from Kulik's theory. The present theory well explains the experimental results for the zero-field step and the Fiske step of long junctions, which could not be explained by the previous theories.