c-axis penetration depth and interlayer conductivity in the thallium-based cuprate superconductors

The c-axis Josephson plasmons in optimally doped single-layer and bilayer high-$T_c$ cuprates ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CuO}}_6$ and ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ have been investigated using infrared spectroscopy. We observed the plasma frequencies for these two compounds at 27.8 and 25.6 ${\mathrm{cm}}^{-1}$ respectively, which we interpret as Josephson resonances across the TlO blocking layers. No maximum in the temperature dependence of the c-axis conductivity was observed below $T_c,$ indicating that even in the superconducting state a coherent quasiparticle contribution to the c-axis conductivity is absent or very weak.