LOW-FREQUENCY ADMITTANCE OF QUANTIZED HALL CONDUCTORS

We present a current and charge conserving theory for the low-frequenc y admittance of a two-dimensional electron gas connected to ideal meta llic contacts and subject to a quantizing magnetic field. In the frame work of the edge-channel picture, we calculate the admittance up to fi rst order with respect to frequency. The transport coefficients in fir st order with respect to frequency, which are called emittances, deter mine the charge emitted into a contact of the sample or a gate in resp onse to an oscillating voltage applied to a contact of the sample or a nearby gate. The emittances depend on the potential distribution insi de 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 electrochemical capacitance matrix, which descr ibes a (fictitious) geometry in which each edge channel is coupled to its own reservoir. The particular relation of the emittance matrix to this electrochemical capacitance matrix depends strongly on the topolo gy of the edge channels: We show that edge channels that connect diffe rent reservoirs contribute with a negative capacitance to the emittanc e. For example, while the emittance of a two-terminal Corbino disk is a capacitance, the emittance of a two-terminal quantum Hall bar is a n egative capacitance. The geometry of the edge-channel arrangement in a many-terminal setup is reflected by symmetry properties of the emitta nce matrix. We investigate the effect of voltage probes and calculate the longitudinal and the Hall resistances of an ideal four-terminal Ha ll bar for low frequencies.