Direct measurement of quantum capacitance transition with variable tunneling barriers

Electrical current measurements on atomic-size systems accessed with Scanning Tunneling Microscope (STM) or Mechanically Controllable Break Junction (MCBJ) techniques\footnote{N. Agra\"{i}t, A. Levy-Yeyati and J.M. van Ruitenbeek. Phys. Rep. 377 (2003), 81.} are commonly studied considering only electrical conductance. Fully impedance (or admittance) measurements on such systems would provide greater understanding and new physical phenomena to be studied. In the present work we show simultaneous conductance-capacitance measurements at variable tunneling junctions. We use STM technique under cryogenic conditions, where vacuum acts as the barrier, and tip and sample consist of faced-sharpened tips made out of the very same pure metal. With a four-probe AC Lock-In technique we provide direct measurements of the quantum transition\footnote{T. Christen and M. B\"uttiker. Phys. Rev. Letters 77 (1996), 1.} from the purely geometrical capacitance (very long distances) to the leak of capacitance when tunneling regime is accessed\footnote{X. Zhao \textit{et al.} Phys. Rev. B 60 (1999), 24.}.