Tunnelling current-voltage characteristics of Angstrom gaps measured with terahertz time-domain spectroscopy

Quantum tunnelling becomes inevitable as gap dimensions in metal structures approach the atomic length scale, and light passing through these gaps can be used to examine the quantum processes at optical frequencies. Here, we report on the measurement of the tunnelling current through a 3-Å-wide metal-graphene-metal gap using terahertz time-domain spectroscopy. By analysing the waveforms of the incident and transmitted terahertz pulses, we obtain the tunnelling resistivity and the time evolution of the induced current and electric fields in the gap and show that the ratio of the applied voltage to the tunnelling current is constant, i.e., the gap shows ohmic behaviour for the strength of the incident electric field up to 30 kV/cm. We further show that our method can be extended and applied to different types of nanogap tunnel junctions using suitable equivalent RLC circuits for the corresponding structures by taking an array of ring-shaped nanoslots as an example.