Dynamic response of a mesoscopic capacitor in the presence of strong electron interactions

TL;DR

This paper investigates the universal relaxation resistance of a one-dimensional mesoscopic capacitor with strong electron interactions, revealing a quantum phase transition and providing theoretical predictions for experimental tests.

Contribution

It combines perturbation theory, renormalization group, and quantum Monte Carlo methods to analyze the entire parameter range of dot-lead coupling in strongly interacting systems.

Findings

Relaxation resistance remains universal under certain conditions.

Identifies a quantum phase transition at Luttinger parameter K<1/2.

Results applicable to quantum dots in fractional quantum Hall edge states.

Abstract

We consider a one dimensional mesoscopic capacitor in the presence of strong electron interactions and compute its admittance in order to probe the universal nature of the relaxation resistance. We use a combination of perturbation theory, renormalization group arguments, and quantum Monte Carlo calculation to treat the whole parameter range of dot-lead coupling. The relaxation resistance is universal even in the presence of strong Coulomb blockade when the interactions in the wire are sufficiently weak. We predict and observe a quantum phase transition to an incoherent regime for a Luttinger parameter $K<1/2$. Results could be tested using a quantum dot coupled to an edge state in the fractional quantum Hall effect.