Nonequilibrium dynamics of a singlet-triplet Anderson impurity near the quantum phase transition

TL;DR

This paper investigates the nonequilibrium dynamics of a singlet-triplet Anderson impurity near a quantum phase transition, revealing conductance jumps, spectral density features, and explaining experimental observations in molecular transport.

Contribution

It introduces a detailed analysis of the singlet-triplet Anderson model near the quantum phase transition, including spectral density calculations and explanations of experimental conductance features.

Findings

Conductance jumps at the quantum phase transition.

Spectral density splits into singlet and triplet components.

Explanation of the three-peak structure in nonequilibrium transport.

Abstract

We study the singlet-triplet Anderson model (STAM) in which a configuration with a doublet is hybridized with another with a singlet and a triplet, as a minimal model to describe two-level quantum dots coupled to two metallic leads in effectively a one-channel fashion. The model has a quantum phase transition which separates regions of a doublet and a singlet ground state. The limits of integer valence of the STAM (which include a model similar to the underscreened spin-1 Kondo model) are derived and used to predict the behavior of the conductance through the system at both sides of the transition, where it jumps abruptly. At a special quantum critical line, the STAM can be mapped to an ordinary Anderson model (OAM) plus a free spin 1/2. We use this mapping to obtain the spectral densities of the STAM as a function of those of the OAM at the transition. Using the non-crossing approximation (NCA), we calculate the spectral densities and conductance through the system as a function of temperature and bias voltage, and determine the changes that take place at the quantum phase transition. The separation of the spectral density into a singlet and a triplet part allows us to shed light on the underlying physics and to explain a shoulder observed recently in the zero-bias conductance as a function of temperature in transport measurements through a single fullerene molecule [Roch N et al., Nature 453, 633 (2008)]. The structure with three peaks observed in nonequilibrium transport in these experiments is also explained.