Theory of macroscopic quantum tunneling in high-Tcc-axis Josephson junctions

Abstract

We study macroscopic quantum tunneling (MQT) in $c$-axis twist Josephson junctions made of high-${T}_{c}$ superconductors in order to clarify the influence of the anisotropic order parameter symmetry (OPS) on MQT. The dependence of the MQT rate on the twist angle $\ensuremath{\gamma}$ about the $c$ axis is calculated by using the functional integral and the bounce method. Due to the $d$-wave OPS, the $\ensuremath{\gamma}$ dependence of standard deviation of the switching current distribution and the crossover temperature from thermal activation to MQT are found to be given by $\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}$ and $\sqrt{\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}}$, respectively. We also show that a dissipative effect resulting from the nodal quasiparticle excitation on MQT is negligibly small, which is consistent with recent MQT experiments using ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ intrinsic junctions. These results indicate that MQT in $c$-axis twist junctions becomes a useful experimental tool for testing the OPS of high-${T}_{c}$ materials at low temperature, and suggest high potential of such junctions for qubit applications.