Electromagnetic coupling in the sub-wavelength metal-insulator-metal (MIM) resonator allows for the engineering of optical responses and the enhancement of localized near-fields. Recent studies have shown that quantum effects, such as the spill-out of electrons and non-local screening, become significant as the insulator gap distance approaches the sub-nanometer scale. In this study, we investigate the plasmon tunneling effects in a sandwich metasurface composed of two cascading periodic MIM resonator arrays. According to theoretical calculations, both tunneling current and tunneling conductiv...