Standing Friedel waves: a quantum probe of electronic states in nanoscale devices.

We report a theoretical study of the dynamic response of electrons in a metallic nanowire or a two-dimensional electron gas under a capacitively coupled "spot gate" driven by an ac voltage. A dynamic standing Friedel wave (SFW) is formed near the spot gate and near edges and boundaries, analogous to the static Friedel oscillations near defects. The SFW wavelength is controlled by the ac voltage frequency and the device's Fermi velocity, whereby the latter can be measured. In addition, the SFW amplitude exhibits resonant behavior at driving frequencies that are related to eigenenergy spacings in the device, allowing their direct measurement.