Theory of macroscopic quantum tunneling in high-Tc cuprate

To reveal macroscopic quantum tunneling (MQT) in high-Tc superconductor Josephson junctions is an important issue since there is a possibility to fabricate a superconducting quantum bit by use of high Tc junctions. Using the functional integral and the instanton theory, we analytically obtain the MQT rate (the inverse lifetime of the metastable state) for the c-axis twist Josephson junctions. In the case of the zero twist angle, the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is suppressed compared with the finite twist angle cases. Furthermore, the effect of the zero energy bound states (ZES) on the MQT in the in-plane junctions is theoretically investigated. We obtained the analytical formula of the MQT rate and showed that the presence of the ZES at the normal/superconductor interface leads to a strong Ohmic quasiparticle dissipation. Therefore, the MQT rate is noticeably inhibited compared with the c-axis junctions in which the ZES are completely absent.