Supercurrent Generation by Spin-twisting Itinerant Motion of Electrons: Re-derivation of the ac Josephson Effect Including the Current Flow Through the Leads Connected to Josephson Junction

Based on a new supercurrent generation mechanism proposed for the cuprate superconductivity (as reported by Koizumi (J. Supercond. Nov. Magn. 24:1997, 2011 ); Hidekata and Koizumi (J. Supercond. Nov. Magn. 24:2253, 2011 ); Koizumi et al. (J. Supercond. Nov. Magn. 27:121, 2014 ); Koizumi et al. (J. Supercond. Nov. Magn. 2014 ), we re-derive the ac Josephson effect including the current flow through the leads connected to the Josephson junction and the impressed electromotive force. It is noted that the actual experimental boundary condition where the Josephson frequency 2 e V 0 / h ( h is Planck’s constant, e is the absolute value of electron charge, and V 0 is the dc voltage across the Josephson junction) is measured differently from the one assumed by Josephson, and 2 e V 0 / h is obtained by the electron tunneling instead of the Cooper pair tunneling. It is also indicated that the standard textbook description for the Josephson relation, “if a dc voltage V 0 is applied, the time-variation of ϕ occurs” (as reported by Feynman et al. ( 1965 ); Ashcroft and Mermin ( 1976 ); Kittel ( 1986 ); Tinkham ( 1996 ) ( ϕ is related to the tunneling current as J s = J c sin ϕ ) should be rephrased, “if the time-variation of ϕ is introduced, a voltage difference V 0 appears.” We show that by adding the Rashba spin-orbit interaction to the Bardeen, Cooper, and Schrieffer (BCS) Hamiltonian, the spin-twisting itinerant motion of electrons is stabilized in the BCS superconductors; thus, it is suggested that the present, new supercurrent generation mechanism is also relevant to the BCS superconductors, i.e., the true origin of the supercurrent generation in the BCS superconductors may also be the spin-twisting itinerant motion of electrons.