Correlated electron physics in multilevel quantum dots: phase transitions, transport, and experiment

TL;DR

This paper investigates the quantum phase transitions, transport properties, and experimental signatures of correlated two-level quantum dots, revealing distinct phases and transitions characterized by Kosterlitz-Thouless and first-order behaviors, with implications for conductance measurements.

Contribution

It provides a comprehensive analysis of phase diagrams, quantum phase transitions, and conductance in multilevel quantum dots with complex electron interactions, including a generalized sum rule and Luttinger's theorem.

Findings

Two main phases: Fermi liquid and underscreened spin-1 fixed point.

Quantum phase transitions are mainly Kosterlitz-Thouless, with some first-order level crossings.

Conductance behavior varies with phase, showing resonance collapse or antiresonance.

Abstract

We study correlated two-level quantum dots, coupled in effective 1-channel fashion to metallic leads; with electron interactions including on-level and inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics and electronic transport properties are considered; and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterised by a normal Fermi liquid fixed point (FP), the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of non-integral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first order level-crossing transitions at high symmetry points. A `Friedel-Luttinger sum rule' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T=0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase; the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.