Frequency-to-voltage converter based on Bloch oscillations in a capacitively coupled GaAs-${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$As quantum well

A charged capacitor which is placed with a semiconductor in a closed loop will normally discharge in a characteristic time τ=1/RC. We show, however, that if a semiconductor of high purity is subjected to a rf bias with frequency ω, discharge does not occur if the voltage across the capacitor is proportional to an integer multiple of ħω/e. Thus a rf frequency may be converted to a dc voltage. The ac to dc conversion is made possible by the interplay between Bloch oscillations induced by the electric field of the external rf source and those induced by the field from the charge residing on the capacitor. The process resembles the frequency-to-voltage conversion by a hysteretic Josephson junction, except that the evolution of the Josephson phase is replaced by the evolution of the crystal momentum of conduction electrons in the semiconductor. We discuss the parameters and conditions for which this behavior may be observed.