High-Field Quasiparticle Tunneling in ${{\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_{2}O}_{8+\mathit{\delta }}$: Negative Magnetoresistance in the Superconducting State

We report on the $c$-axis resistivity ${\rho }_c\left(H\right)$ in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ that peaks in quasistatic magnetic fields up to 60 T. By suppressing the Josephson part of the two-channel (Cooper pair/quasiparticle) conductivity ${\sigma }_c\left(H\right)$, we find that the negative slope of ${\rho }_c\left(H\right)$ above the peak is due to quasiparticle tunneling conductivity ${\sigma }_q\left(H\right)$ across the ${\mathrm{CuO}}_2$ layers below $H_{c2\mathrm{}}$. At high fields (a) ${\sigma }_q\left(H\right)$ grows linearly with $H$, and (b) ${\rho }_c\left(T\right)$ tends to saturate ( ${\sigma }_c\ne 0$) as $T\to 0$, consistent with the scattering at the nodes of the $d$-wave gap. A superlinear ${\sigma }_q\left(H\right)$ marks the normal state above $T_c$.