Limiting current density in a crossed-field nanogap

Using a mean-field theory, we have studied the quantum extension on the limiting current density in a crossed-field nanogap. When the gap spacing is less than the electron wavelength, our results show that the limiting current density is increased by a large factor from the classical values due to the effects of electron tunneling. The effects of the external magnetic field diminish with a decrease of gap spacing. Smooth transition from the classical regime to the quantum regime is demonstrated.