Quantum decay of the supercurrent and intrinsic capacitance of Josephson junctions beyond the tunnel limit

Abstract

A nondissipative supercurrent state of a Josephson junction is metastable with respect to the formation of a finite-resistance state. This transition is driven by fluctuations, thermal at high temperatures and quantum at low temperatures. We evaluate the lifetime of such a state due to quantum fluctuations in the limit when the supercurrent is approaching the critical current. The decay probability is determined by the instanton action for the superconducting phase difference across the junction. At low temperatures, the dynamics of the phase is massive and is determined by the effective capacitance, which is a sum of the geometric and intrinsic capacitance of the junction. We model the central part of the Josephson junction either by an arbitrary short mesoscopic conductor described by the set of its transmission coefficients, or by a diffusive wire of an arbitrary length. The intrinsic capacitance can generally be estimated as ${C}_{*}\ensuremath{\sim}G/{E}_{g}$, where $G$ is the normal-state conductance of the junction and ${E}_{g}$ is the proximity minigap in its normal part. The obtained capacitance is sufficiently large to qualitatively explain the hysteretic behavior of the current-voltage characteristic even in the absence of overheating.