Dynamic and nonlinear transport in mesoscopic structures

Abstract

In this chapter we discuss the capacitance, the linear low-frequency admittance and the weakly nonlinear DC transport of low-dimensional and phase-coherent conductors. Of special interest are quantized Hall samples, the quantum point contact, and the resonant tunnelling barrier. Dynamic and nonlinear transport is a challenging subject since a consistent treatment requires knowledge of the nonequilibrium state. In contrast, the linear static response (DC conductance) of a mesoscopic sample is determined by the equilibrium state only. Once the equilibrium potential is known the transmission and reflection probabilities of electrons in this potential can be calculated. The transmission behaviour of a sample completely specifies its DC conductance. Naturally from such a discussion we learn nothing about the charge density and current distribution inside the mesoscopic conductor. However, the dynamic response and the nonlinear response of a conductor depend on the charge and current distributions established away from equilibrium. Dynamic and nonlinear transport can thus be viewed as a probe of the charge response of the conductor. The dynamic response and the nonlinear response reveal information which is not accessible by linear DC measurements.