Multiple-valued $c$-axis critical current and phase locking in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\mathrm{\delta }}$ single crystals

We have experimentally found that the temperature dependence of the critical current in the $c$-axis direction, $I_c\mathrm{}\left(T\right),$ of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\mathrm{\delta }}$ (Bi2212) single crystals may have multiple branches. At a given temperature, the probability distribution function ${P(I}_c)$ for leaving the zero-voltage state may therefore have several maxima, each corresponding to a particular branch of $I_c\mathrm{}\left(T\right).$ We have modeled the $I_c\mathrm{}\left(T\right)\mathrm{}$ for Bi2212, considering it as a stack of intrinsic Josephson junctions (JJ’s). The numerical simulations are in qualitative agreement with the experiment. We argue that the existence of different quasiequilibrium fluxon modes in stacked JJ’s may be a reason for the multiple-valued $I_c$ that is observed in the experiments. Mutual phase locking of junctions, resulting in an increased $I_c\mathrm{}\left(T\right),$ is observed.