Non-adiabatic electron pumping driven by continuous bias voltage modulation

Recent developments in nanotechnology enable us to control and observe electron transfer with high accuracy fulfilling needs for quantum metrology. One of its important instances is an electron pump driven by a time periodic bias voltage between source and drain electrodes attached to a microscopic system such as a quantum dot (J. P. Pekola et al., Rev. Mod. Phys. 85, 1421 (2013)). In conventional studies, the electron pump has been mostly formulated in an adiabatic regime, where the time-dependent bias is described by an infinitely slow modulation of electrochemical potentials of electrodes (T. Yuge et al., Phys. Rev. B 86, 235308 (2012)). This formalism is, however, practically useless because the pumped current generated by the infinitely slow modulation is zero in a strict sense. The purpose of the present study is to provide a more realistic formalism describing the pumping under a finite speed continuous modulation of the bias voltage. To this end, we propose an extended formalism of the pumping based on the full counting statistics with quantum master equation taking into account a temporal shift of single-particle energy of electrons in source and drain induced by the voltage modulation.