C-axis coupling in underdopedBi2Sr2CaCu2O8+δwith varying degrees of disorder

Abstract

The dependence of the Josephson plasma resonance (JPR) frequency in heavily underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ on temperature and controlled pointlike disorder, introduced by high-energy electron irradiation, is cross-correlated and compared to the behavior of the $ab$-plane penetration depth. It is found that the square of the zero-temperature plasma frequency, representative of the superfluid component of the $c$-axis spectral weight, decreases proportionally with ${T}_{c}$ when the disorder is increased. The temperature dependence of the JPR frequency is the same for all disorder levels, including pristine crystals. The reduction of the $c$-axis superfluid density as function of disorder is accounted for by pair breaking induced by impurity scattering in the $\mathrm{Cu}{\mathrm{O}}_{2}$ planes, rather than by quantum fluctuations of the superconducting phase. The reduction of the $c$-axis superfluid density as function of temperature follows a ${T}^{2}$ law and is accounted for by quasiparticle hopping through impurity-induced interlayer states.