Quantum inductance and negative electrochemical capacitance at finite frequency in a two-plate quantum capacitor

We report on theoretical investigations of frequency-dependent quantum capacitance. It is found that at finite frequency, a quantum capacitor can be characterized by a classical RLC circuit with three parameters: a static electrochemical capacitance, a charge relaxation resistance, and a quantum inductance. The quantum inductance is proportional to the characteristic time scale of electron dynamics, and due to its existence, the time-dependent current can accumulate a phase delay and lags behind the applied ac voltage, leading to a negative effective capacitance.