Absence of fractional ac Josephson effect in superconducting junctions

Physical Review B: Condensed Matter and Materials Physics. 2024. Vol. 110. No. 13. Article 134521.

Kalenkov M., Andrei D. Zaikin

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 2π periodic in the Josephson
phase ϕ in full accordance with general principles. Our result unambiguously argues against the idea of the
so-called “fractional ac Josephson effect” admitting 4π periodic in ϕ CPR. We also demonstrate that at any
nonzero 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 nontrivial 2π-periodic dissipative current with the amplitude ∝|V |1/3.

Keywords: эффект Джозефсона, Josephson effect, quantum dissipation, Andreev levels, квантовая диссипация, уровни Андреева, superconductivity and hybrid structures, сверхпроводимость и гибридные структуры