| We discuss the capacitance and the resistance, usually called the charge relaxation resistance, of a quantum coherent RC circuit driven by a low-frequency AC voltage. This circuit is the quantum analogue of the classical RC circuit: it comprises a dot capacitively coupled to a nearby gate and connected to a single reservoir lead. As a result of phase coherence and electronic interactions, the quantum circuit behaves quite differently and Kirchhoff's law is violated. Here we show that the charge relaxation resistance is perfectly quantized, regardless of the single lead transmission and for an arbitrary strength of the interaction. Its low-frequency value is h/2 e2. When the driving frequency exceeds the dot level spacing, we predict a transition to a metallic regime with a doubled quantized resistance h/e2. The novel quantized resistance h/e2 is connected to the Korringa-Shiba relation of the Kondo model, thereby revealing the physics behind these universal charges. |
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