Strongly correlated dynamics in multichannel quantum RC circuits

TL;DR

This paper investigates the dissipation and charge-relaxation resistance in multichannel quantum RC circuits, revealing universal behavior at low temperatures and analyzing effects of asymmetry and backscattering through theoretical models.

Contribution

It demonstrates the universality of charge-relaxation resistance in multichannel quantum RC circuits and maps the system to an effective one-channel Kondo model for analysis.

Findings

Charge-relaxation resistance becomes universal at low temperatures.

Mapping to a one-channel Kondo model explains the universality.

Backscattering effects influence transport properties in the two-channel case.

Abstract

We examine dissipation effects in a multichannel quantum RC circuit, comprising a cavity or single-electron box capacitively coupled to a gate and connected to a reservoir lead via several conducting channels. Depending on the engineering details of the quantum RC circuit, the number of channels contributing to transport vary, as do the form of the interchannel couplings. For low-frequency AC transport, the charge-relaxation resistance ($R_{q}$) is a nontrivial function of the parameters of the system. However, in the vicinity of the charge degeneracy points and for weak tunneling, we find as a result of cross-mode mixing or channel asymmetry that $R_q$ becomes universal for a metallic cavity at low temperatures, and equals the unit of quantum resistance. To prove this universality we map the system to an effective one-channel Kondo model, and construct an analogy with the Coulomb gas. Next, we probe the opposite regime of near-perfect transmission using a bosonization approach. Focussing on the two-channel case, we study the effect of backscattering at the lead-dot interface, more specifically, the role of an asymmetry in the backscattering amplitudes, and make a connection with the weak tunneling regime near the charge degeneracy points.