Josephson-vortex states in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$

Josephson-vortex (JV) states have been studied by measuring the flow resistance in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$ (Bi-2212) as a function of the parallel magnetic field with the current along the $c$-axis. From the periodic oscillations, we can assign the three-dimensionally long-range-ordered state (3DLOS) of JVs (PRL\textbf{89}, 247002(2002), Physica \textbf{C412-414}, 454(2004)). The lower and upper boundaries of 3DLOS were determined from the magnetic field of beginning and stopping in the oscillations, respectively. From the flow resistance and the $I-V$ characteristics measurements crossing the upper boundary, we suggest that the JVs are in ordered state in \textit{in-plane}, but have less ordering along the $c$-axis. This JV state may correspond to the 2D-quasi-long-range ordered state, proposed by Hu{\&}Tachiki (PRB\textbf{70}, 064506(2004)).