A quantum criticality perspective on the charging of narrow quantum-dot levels

TL;DR

This paper explores the charging behavior of narrow quantum-dot levels with interactions, revealing a power-law dependence on tunneling amplitude through an analogy with the Kondo model, supported by analytical and numerical methods.

Contribution

It introduces a novel analogy between quantum-dot charging and the anisotropic Kondo model, providing explicit analytical expressions for the crossover scale.

Findings

Charging exhibits a power-law dependence on tunneling amplitude.

Analytical expressions for the crossover exponent are derived.

Numerical and renormalization-group calculations confirm the analytical results.

Abstract

Understanding the charging of exceptionally narrow levels in quantum dots in the presence of interactions remains a challenge within mesoscopic physics. We address this fundamental question in the generic model of a narrow level capacitively coupled to a broad one. Using bosonization we show that for arbitrary capacitive coupling charging can be described by an analogy to the magnetization in the anisotropic Kondo model, featuring a low-energy crossover scale that depends in a power-law fashion on the tunneling amplitude to the level. Explicit analytical expressions for the exponent are derived and confirmed by detailed numerical and functional renormalization-group calculations.