  By feeding current into the topmost $\mathrm{Cu_2O_4}$-layer of a mesa etched
into the surface of a $\mathrm{Bi_2Sr_2CaCu_2O_{8+x}}$ (BSCCO) single crystal,
we measured its superconducting critical value from a sharp upturn or break in
current-voltage characteristics of the mesas. From this, we estimate the sheet
critical current density of a single $\mathrm{Cu_2O_4}$ plane to be $\sim$\
0.3-0.7 A/cm at 4.5 K, corresponding to the bulk current density of $2-5\
\mathrm{MA/cm^2}$. These values are among the largest ever measured for BSCCO
single crystals, thin films and tapes.
