Josephson effects in weakly coupled MgB₂ intergrain nanobridges prepared by focused ion beam

We have fabricated weakly coupled intergrain nanobridges from MgB₂ films by a focused ion beam (FIB) patterning technique and studied their transition properties. The bridges were nominally 300 nm wide and 100 nm long, and crossed a single grain boundary perpendicularly. The temperature-dependent resistance data showed a two-step transition after FIB pattern with more-than-two-decade increase in the resistivity. Current-voltage curves showed the characteristics of an ideal Josephson junction. The measured data were perfectly matched with the theory of the resistively shunted junction model with thermal fluctuations at all measured temperatures. At 4.2 K, the measured data showed the effect of hysteresis in agreement with the estimated McCumber parameter β_c≫0.3. The hysteresis effect disappeared above 6 K. The critical currents obtained from fitting to the RSJ model were linearly dependent on temperature, implying that the grain boundary played an insulating barrier.