Breathing charge density waves in intrinsic Josephson junctions

We demonstrate the creation of a charge density wave (CDW) along a stack of coupled Josephson junctions (JJs) in layered superconductors. Electric charge in each superconducting layer oscillates around some average value, forming a breathing CDW. We show the transformation of a longitudinal plasma wave to CDW in the state corresponding to the outermost branch. Transition between different types of CDW's related to the inner branches of $IV$-characteristic is demonstrated. The effect of the external electromagnetic radiation on the states corresponding to the inner branches differs crucially from the case of the single JJ. The Shapiro steps in the $IV$-characteristics of the junctions in the stack do not correspond directly to the frequency of radiation $\omega$. The system of JJs behaves like a single whole system: the Shapiro steps or their harmonics in the total $IV$-characteristics appear at voltage $\sum V_l=N_R\frac{m}{n}\omega$, where $V_l$ is the voltage in $l$-th junction, $N_R$ is the number of JJs in the rotating state, and $m$ and $n$ are integer numbers.