Quantum Charge Dynamics in an Array of Intrinsic Josephson Junctions

We present a theory for the c-axis charge dynamics in a stack of underdamped intrinsic Josephson-junctions with a finite in-plane area, W. It is shown that the size effect with respect to W can be described as a quantum effect in the phase dynamics of a Josephson-junction array. We derive rigorously the capacitance matrix of a 1D Josephson-junction array on the basis of the time-dependent Ginzburg-Landau model at T = 0 K. The long range part of the Coulomb interaction between superconducting charges induces the plasma oscillations with a finite gap propagating along the c-axis. The plasma oscillations, which are stable in systems with large W, become unstable at a critical in-plane area. W_c, as the in-plane area decreases. The instability is caused by the Coulomb blockade effect. In the systems with W < W_c the single Cooper-pair tunneling dominates the charge dynamics. We develop a renormalization group theory for the charge dynamics of a 1D array of Josephson-junctions and derive the explicit expression for W_c. In the limit of small W our theory predicts the charge soliton state. The size of the charge soliton is related to the charge screening length of the superconducting electron system. The edge voltage in the charge soliton state is proportional to the number of junctions in an array.