Theory of the superconducting phase and charge dynamics in intrinsic Josephson-junction systems: microscopic foundation for longitudinal Josephson plasma and phenomenological dynamical equations

Abstract

The purpose of this paper is to present microscopic theory for intrinsic Josephson junctions and provide proper model equations describing macroscopic longitudinal and transverse dynamics in intrinsic Josephson junctions. We start with BCS functional integral formalism and clarify that fluctuations around the Josephson relation have an important role in low-energy fluctuations when the superconducting layer thickness is decreased to atomic scale comparable to the charge screening length. Intrinsic Josephson junctions completely fulfill such condition, in which the longitudinal plasma excitation mode propagating along the stacking direction is proved to exist. On the other hand, we derive the most basic dynamical equations for the superconducting phase and charge based on Euler–Lagrange equations obtained from effective action and show that the equations can be reduced to the phenomenological coupled Sine–Gordon equation and Koyama–Tachiki model under proper approximations considering two typical experimental situations.