Capacitance of a resonant level coupled to Luttinger liquids

TL;DR

This paper investigates the differential capacitance of a quantum dot coupled to Luttinger liquids or fractional quantum Hall edges, revealing divergence behaviors linked to two-channel Kondo physics that enable parameter extraction.

Contribution

It demonstrates how capacitance divergence patterns can be used to probe Luttinger liquid parameters through thermodynamic measurements.

Findings

Capacitance exhibits logarithmic or power-law divergence at low temperatures.

Divergence behavior occurs over a broad parameter space, including at filling factor 1/3.

Results connect capacitance behavior to generalized two-channel Kondo physics.

Abstract

In this paper we study the differential capacitance of a single-level quantum dot attached to quantum wires in the Luttinger liquid phase, or to fractional quantum Hall edges, by both tunneling and interactions. We show that logarithmic or even power-law divergence of the capacitance at low temperatures may result in a substantial region of the parameter space (including the $\nu=1/3$ filling). This behavior is a manifestation of generalized two channel Kondo physics, and can be used to extract Luttinger liquid parameters from thermodynamic measurements.