This project is focused on dynamics of the phase difference across Josephson junction. In low Tc superconductor junctions, this dynamics is described with the Hamiltonian
H = ECn2 – EJ(φ),
where n is the charge on the junction capacitor, and EJ(φ) is the Josephson energy. This form of the macroscopic Hamiltonian is only valid for superconductors with large energy gap compared to typical frequency of phase fluctuation. Due to a large energy gap, the quasiparticle transitions induced by phase fluctuations are exponentially suppressed, and therefore dissipation effects are negligible.
The situation in high-Tc superconductors is different. The d-wave symmetry of the order parameter allows for low energy Andreev bound states, mid-gap states (MGS). These states are strongly coupled to the phase degree of freedom, and become strongly non-equilibrium under the influence of phase fluctuation. Therefore, the macroscopic dynamics in high-Tc junctions is much more complex and does not obey the Hamiltonian presented above. We explore various regimes of joint evolution of the superconducting phase and MGS.
More information: J. Michelsen and V.S. Shumeiko, Quantum Phase Dynamics of High-Tc Josephson Junctions, J. Phys. Conf. Series, 150, 052159 (2009).