Reentrance Effect in Macroscopic Quantum Tunneling and Nonadiabatic Josephson Dynamics in $d$-Wave Junctions

We develop a theoretical description of nonadiabatic Josephson dynamics in superconducting junctions containing low energy quasiparticles. Within this approach we investigate the effects of midgap states in junctions of unconventional $d$-wave superconductors. We identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling, and connect this phenomenon to the experimental observations in Phys. Rev. Lett. 94, 087003 (2005). It is also shown that nonlinear Josephson dynamics can be defined by resonant interaction with midgap states reminiscent of nonlinear optical phenomena in media of two-level atoms.

Figure 1

Reentrance effect in MQT. Sketch of temperature dependence of decay rate (wide shadow line) illustrates the effect featuring three transitions between thermal activation and MQT regimes. Experimental transition temperatures are given by zeros of function $F(x)$, defined in the text [dark gray (blue) line] for $\eta =38$. Lower inset shows development of nonmonotonic feature of function $F(x)$ with increasing $\eta$, at $\eta >25$. Upper inset illustrates junction geometry and scattering electron trajectory (dashed line).

Figure 2

Effect of MGS on nonlinear resonance response of the junction. Response amplitude as function of detuning is shown for different amplitudes of driving current. Inset: Maximum response amplitude as a function of driving current, dots indicate current values in the main figure.