c-axis transport and phenomenology of the pseudo-gap state in $Bi_2Sr_2CaCu_2O_{8+\delta}$

TL;DR

This study investigates the c-axis resistivity and carrier participation in Bi-2212 crystals across various doping levels, revealing a universal behavior in carrier localization and the effects of magnetic fields on superconducting coherence.

Contribution

It introduces a universal scaling of carrier participation with temperature and doping, and shows magnetic fields do not alter in-plane localization but affect phase coherence.

Findings

Carrier fraction $ abla(T, ext{doping})$ collapses onto a universal curve.

At the superconducting transition, the non-participating carrier fraction is doping independent.

Magnetic fields up to 14 T do not change in-plane localization but extend the temperature range of scaling.

Abstract

We measure and analyze the resistivity of $Bi_2Sr_2CaCu_2O_{8+\delta}$ crystals for different doping $\delta$. We obtain the fraction of carrier $\eta(T,\delta) = n_g/n_{TOT}$ that do not participate to the c-axis conductivity. All the curves $\eta(T,\delta)$ collapse onto a universal curve when plotted against a reduced temperature $x=[T-\Theta(\delta)]/\Delta^{*}(\delta)$. We find that at the superconducting transition $n_g$ is doping independent. We also show that a magnetic field up to 14 T does not affect the degree of localization in the (a,b) planes but widens the temperature range of the x-scaling by suppressing the superconducting phase coherence.