Universal Resistances of the Quantum RC circuit

TL;DR

This paper investigates the universal quantized resistance in a quantum RC circuit, revealing how it varies with frequency and cavity size, and links it to strongly correlated electron systems.

Contribution

It demonstrates the universality of charge relaxation resistance across transmission regimes and establishes a connection with the Kondo model, advancing understanding of quantum coherence effects.

Findings

Resistance is quantized at h/2e^2 and h/e^2 depending on frequency.

Charge relaxation resistance is universal for a broad class of models.

The resistance relates to the Kondo model's Shiba relation.

Abstract

We examine the concept of universal quantized resistance in the AC regime through the fully coherent quantum RC circuit comprising a cavity (dot) capacitively coupled to a gate and connected via a single spin-polarized channel to a reservoir lead. As a result of quantum effects such as the Coulomb interaction in the cavity and global phase coherence, we show that the charge relaxation resistance $R_q$ is identical for weak and large transmissions and it changes from $h/2e^2$ to $h/e^2$ when the frequency (times $\hbar$) exceeds the level spacing of the cavity; $h$ is the Planck constant and $e$ the electron charge. For large cavities, we formulate a correspondence between the charge relaxation resistance $h/e^2$ and the Korringa-Shiba relation of the Kondo model. Furthermore, we introduce a general class of models, for which the charge relaxation resistance is universal. Our results emphasize that the charge relaxation resistance is a key observable to understand the dynamics of strongly correlated systems.