Quantum saturation of capacitance in metals

There are two contributions to the electronic capacitance in between two electrodes. First, there is the classical capacitive effect as an electric field is being developed in between these. Another contribution, which has often been neglected for metals, is related to the Pauli exclusion principle for the difficulty to accumulate charges on the electrode surface, the so-called quantum capacitance [T. Christen and M. Büttiker. Phys. Rev. Letters 77 (1996), 1]. Here we report the use of a Scanning Tunneling Microscope at low temperatures to study the variations of the capacitance as we approach two metallic electrodes made of Pt or Au. Three regimes are clearly visible in this process: A classical increase of capacitance which at short distances turn to saturation to the quantum capacitance limit, and finally, a leak of capacitance due to quantum tunneling.