Controlling the Intrinsic Josephson Junction Number in a $\mathbf{Bi_2Sr_2CaCu_2O_{8+\delta}}$ Mesa

In fabricating $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ intrinsic Josephson junctions in 4-terminal mesa structures, we modify the conventional fabrication process by markedly reducing the etching rates of argon ion milling. As a result, the junction number in a stack can be controlled quite satisfactorily as long as we carefully adjust those factors such as the etching time and the thickness of the evaporated layers. The error in the junction number is within $\pm 1$. By additional ion etching if necessary, we can controllably decrease the junction number to a rather small value, and even a single intrinsic Josephson junction can be produced.