Leveraging on analyses of Hamiltonian dynamics to examine the ion motion, we explicitly demonstrate that the proton sheet crossing and plateau-type energy spectrum are two intrinsic features of the effectively accelerated proton beams driven by a drift quasistatic longitudinal electric field. Via two-dimensional particle-in-cell simulations, we show the emergence of proton sheet crossing in a relativistically transparent plasma foil irradiated by a linearly polarized short pulse with the power of one petawatt. Instead of successively blowing the whole foil forward, the incident laser pulse readily penetrates through the plasma bulk, where the proton sheet crossing takes place and the merged self-generated longitudinal electric field traps and reflects the protons to yield a group of protons with plateau-type energy spectrum.