Dynamical Josephson Effect Between a Singlet and a Triplet Superconductor

Phase-sensitive Josephson effect has long been central to identifying unconventional pairing symmetries in superconductors. Although the selection rules governing Josephson junctions (JJs) are generally determined by the symmetries of the constituent superconductors, we demonstrate that this paradigm is modified in the dynamic regime. By modeling a JJ where spin-singlet and spin-triplet superconductors are separated by a two-dimensional electron gas, we show that a time-dependent gate voltage qualitatively changes the underlying selection rules. This modification arises as a consequence of the gate-controlled spin-orbit coupling. A harmonic modulation of the gate voltage generates an oscillatory $\cos \phi$ Josephson component which vanishes in the static limit. The resulting charge current contains both dissipationless and dissipative components, with the latter strongly suppressed at low temperatures. This dynamical Josephson effect could transform the use of JJs in qubits, as sources of spin-triplet currents, and as platforms for proximity effects.