Resistive Hysteresis and NonlinearI−VCharacteristics at the First-Order Melting of the Abrikosov Vortex Lattice

We study a three-dimensional network of Josephson junctions in a magnetic field, which undergoes a first-order melting transition of the triangular vortex lattice. We perform a Langevin dynamics calculation of the resistance and current-voltage ($I-V$) characteristics. We find hysteresis in the resistance as a function of temperature as measured in untwinned Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. Close to the melting temperature the $I-V$ curves are $S$ shaped with hysteresis and show a melting transition when increasing the current, driven by the blowing out of current nucleated vortex loops.