DYNAMIC ADMITTANCE OF MESOSCOPIC CONDUCTORS - DISCRETE-POTENTIAL MODEL

We present a discussion of the low-frequency admittance of mesoscopic conductors in close analogy with the scattering approach to do conduct ance. The mesoscopic conductor is coupled via contacts and gates to a macroscopic circuit which contains ac-current sources or ac-voltage so urces. We find the admittance matrix which relates the currents at the contacts of the mesoscopic sample and of nearby gates to the voltages at these contacts. The problem is solved in two steps: we first evalu ate the currents at the sample contacts in response to the oscillating voltages at the contacts, keeping the internal electrostatic potentia l fixed. In a second stage an internal response due to the potential i nduced by the injected charges is evaluated. The self-consistent calcu lation is carried out for the simple limit in which each conductor is characterized by a single induced potential. Our discussion treats the conductors and gates on equal footing. Since our approach includes al l conductors on which induced fields can change the charge distributio n, the admittance of the total response is current conserving, and the current response depends only on ac-voltage differences. We apply our approach to a mesoscopic capacitor for which each capacitor plate is coupled via a lead to an electron reservoir. We find an electrochemica l capacitance with density-of-state contributions in series with the g eometrical capacitance. The dissipative part of the admittance is gove rned by a charge-relaxation resistance which is a consequence of the d ynamics of the charge pileup one the capacitor plates. We specialize o n a geometry displaying an Aharonov-Bohm effect only at nonzero freque ncies. For a double barrier with a well coupled capacitively to a gate the low-frequency admittance terms may have either sign, reflecting e ither a capacitive or a kinetic-inductive behavior. The validity of a second-quantization-current-operator expression which neglects spatial information is examined for perfect leads in both the frequency and t he magnetic-field domain.