We use the scattering approach to investigate the nonlinear current-voltage characteristic of mesoscopic conductors. We discuss the leading nonlinearity by taking into account the self-consistent nonequilibrium potential. We emphasize conservation of the overall charge and current which are connected to the invariance under a global voltage shift (gauge invariance). As examples, we discuss the rectification coefficient of a quantum point contact and the nonlinear current-voltage characteristic of a resonant level in a double barrier structure.

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The response of an arbitrary scattering problem to quasi-static perturbations in the scattering potential is naturally expressed in terms of a set of local partial densities of states and a set of sensitivities each associated with one element of the scattering matrix. We define the local partial densities of states and the sensitivities in terms of functional derivatives of the scattering matrix and discuss their relation to the Green's function. Certain combinations of the local partial densities of states represent the injectivity of a scattering channel into the system and the emissivity into a scattering channel. It is shown that the injectivities and emissivities are simply related to the absolute square of the scattering wave-function. We discuss also the connection of the partial densities of states and the sensitivities to characteristic times. We apply these concepts to a δ-barrier and to the local Larmor clock.

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We present a current and charge conserving theory for the low frequency admittance of a quantum point contact. We derive expressions for the electrochemical capacitance and the displacement current. The latter is determined by the emittance which equals the capacitance only in the limit of vanishing transmission. With the opening of channels the capacitance and the emittance decrease in a step-like manner in synchronism with the conductance steps. For vanishing reflection, the capacitance vanishes and the emittance is negative.

We present a current and charge conserving theory for the low frequency admittance of a two-dimensional electron gas connected to ideal metallic contacts and subject to a quantizing magnetic field. In the framework of the edge-channel picture, we calculate the admittance up to first order with respect to frequency. The transport coefficients in first order with respect to frequency, which are called emittances, determine the charge emitted into a contact of the sample or a gate in response to an oscillating voltage applied to a contact of the sample or a nearby gate. The emittances depend on the potential distribution inside the sample which is established in response to the oscillation of the potential at a contact. We show that the emittances can be related to the elements of an electro-chemical capacitance matrix which describes a (fictitious) geometry in which each edge channel is coupled to its own reservoir. The particular relation of the emittance matrix to this electro-chemical capacitance matrix depends strongly on the topology of the edge channels: We show that edge channels which connect different reservoirs contribute with a negative capacitance to the emittance. For example, while the emittance of a two-terminal Corbino disc is a capacitance, the emittance of a two-terminal quantum Hall bar is a negative capacitance. The geometry of the edge-channel arrangement in a many-terminal setup is reflected by symmetry properties of the emittance matrix. We investigate the effect of voltage probes and calculate the longitudinal and the Hall resistances of an ideal four-terminal Hall bar for low frequencies.Comment: 26 pages, 5 Figure