Coupling between Phonons and Intrinsic Josephson Oscillations in Cuprate Superconductors

The recently reported subgap structures in the current-voltage characteristic of intrinsic Josephson junctions in the high- $T_c$ superconductors ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ are explained by the coupling between $c$-axis phonons and Josephson oscillations. A model is developed where $c$-axis lattice vibrations between adjacent superconducting multilayers are excited by the Josephson oscillations in a resistive junction. The voltages of the lowest structures correspond well to the frequencies of longitudinal $c$-axis phonons with large oscillator strength in the two materials, providing a new measurement technique for this quantity.