Absence of "fractional ac Josephson effect" in superconducting junctions

Abstract

We develop a microscopic theory of ac Josephson effect in superconducting junctions described by an arbitrary scattering matrix that may include magnetic effects. In the limit of constant in time bias voltage $V$ applied to the junction we derive a formally exact current-phase relation (CPR) that is manifestly $2\pi$-periodic in the Josephson phase $\phi$ in full accordance with general principles. This our result unambiguously argues against the idea of the so-called "fractional ac Josephson effect" admitting $4\pi$-periodic in $\phi$ CPR. We also demonstrate that at any non-zero $V$ quantum dynamics of Andreev bound states becomes non-Hermitian which signals their instability, thus making any 'quasi-equilibrium' description of ac Josephson effect unreliable. We specifically address the limit of highly transparent junctions with magnetic scattering where -- along with super- and excess current terms -- at small $V$ we also recover a non-trivial $2\pi$-periodic dissipative current with the amplitude $\propto |V{|}^{1/3}$

arXiv comment16 pages, 2 figures

References in corpus (17)

• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Quasiclassical Green's function approach to mesoscopic superconductivity
• AC JOSEPHSON EFFECT IN A SINGLE QUANTUM CHANNEL
• $4\pi$-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
• Fractional ac Josephson effect in p- and d-wave superconductors
• Distribution functions in non-equilibrium theory of superconductivity and Andreev spectroscopy in unconventional superconductors
• Interplay of spin-discriminated Andreev bound states forming the 0-$\pi$ transition in Superconductor-Ferromagnet-Superconductor Junctions
• Nonequilibrium Superconductivity near Spin Active Interfaces
• Missing Shapiro steps in topologically trivial Josephson Junction on InAs quantum well
• Josephson junction dynamics in the presence of $2\pi$- and $4\pi$-periodic supercurrents
• Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions
• Adiabatic Dynamics of Superconducting Quantum Point Contacts
• Interaction and Quantum Decoherence
• Manipulation with Andreev states in spin active mesoscopic Josephson junctions
• Fractional charges in conventional sequential electron tunneling
• Fractional Shapiro steps without fractional Josephson effect
• Josephson dynamics at high transmissions: Perturbation theory

Cited by in corpus (1)

• Landau-Zener tunneling and quantum interference of Andreev states