Tunneling spectroscopy with intrinsic Josephson junctions in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\mathrm{\delta }}$ and ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\mathrm{\delta }}$

The paper presents a detailed discussion of the current-voltage characteristic of intrinsic Josephson junctions in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\mathrm{\delta }}$ and ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\mathrm{\delta }}$. In these materials Josephson tunnel junctions are formed naturally between adjacent superconducting CuO${}_2$ bilayers or trilayers. A typical sample consists of a stack of Josephson junctions. We explicitly show that all junctions inside a given sample have identical tunneling characteristics. We discuss the shape (general curvature) of the current-voltage characteristic in terms of a superconducting order parameter that has a predominant $d_{x^2-y^2}$ symmetry. The $I_c{R}_n$ product of the intrinsic Josephson junctions turns out to be 2–3 mV, about 10% of the maximum energy gap ${\Delta }_0/e$. The current-voltage characteristic of every individual junction exhibits pronounced structures in the subgap regime. They are best explained by a recently proposed resonant coupling mechanism between infrared active optical $c$-axis phonons and oscillating Josephson currents.