Wigner Function Description of the A.C.-Transport Through a Two-Dimensional Quantum Point Contact

Abstract

We have calculated the admittance of a two-dimensional quantum point contact (QPC) using a novel variant of the Wigner distribution function (WDF) formalism. In the semiclassical approximation, a Boltzman-like equation is derived for the partial WDF describing both propagating and nonpropagating electron modes in an effective potential generated by the adiabatic QPC. We show that this quantum kinetic approach leads to the well-known stepwise behavior of the real part of the admittance (the conductance), and of the imaginary part of the admittance (the emittance), in agreement with the latest results, which is determined by the number of propagating electron modes. It is shown, that the emittance is sensitive to the geometry of the QPC, and can be controlled by the gate voltage. We established that the emittance has contributions corresponding to both quantum inductance and quantum capacitance. Stepwise oscillations in the quantum inductance are determined by the harmonic mean of the velocities for the propagating modes, whereas the quantum capacitance is a significant mesoscopic manifestation of the non-propagating (reflecting) modes.

23 pages (latex), 3 figures

References in corpus (7)

• Time-dependent transport in interacting and non-interacting mesoscopic systems
• Gauge invariant nonlinear electric transport in mesoscopic conductors
• Low frequency admittance of a quantum point contact
• Low-frequency admittance of quantized Hall conductors
• Time-Dependent Current Partition in Mesoscopic Conductors
• Frequency dependent admittance of a two-dimensional quantum wire
• Spectroscopy of the Potential Profile in a Ballistic Quantum Constriction

Cited by in corpus (1)

• GHz operation of a quantum point contact using stub impedance matching circuit