Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach

TL;DR

This paper develops and compares non-equilibrium cluster methods to analyze the steady-state electronic properties of a quantum dot under bias, revealing how interaction strength affects current, spectral features, and stability diagrams.

Contribution

It introduces the non-equilibrium Variational Cluster Approach for quantum dots and demonstrates its improved accuracy over Cluster Perturbation Theory at higher interactions.

Findings

Good agreement with Matrix Product State benchmarks for low to medium interactions

Interaction-dependent splitting and broadening of the Kondo resonance

Stability diagrams match recent experimental data

Abstract

We calculate steady-state properties of a strongly correlated quantum dot under voltage bias by means of non-equilibrium Cluster Perturbation Theory and the non-equilibrium Variational Cluster Approach, respectively. Results for the steady-state current are benchmarked against data from accurate Matrix Product State based time evolution. We show that for low to medium interaction strength, non-equilibrium Cluster Perturbation Theory already yields good results, while for higher interaction strength the self-consistent feedback of the non-equilibrium Variational Cluster Approach significantly enhances the accuracy. We report the current-voltage characteristics for different interaction strengths. Furthermore we investigate the non-equilibrium local density of states of the quantum dot and illustrate that within the variational approach a linear splitting and broadening of the Kondo resonance is predicted which depends on interaction strength. Calculations with applied gate voltage, away from particle hole symmetry, reveal that the maximum current is reached at the crossover from the Kondo regime to the doubly-occupied or empty quantum dot. Obtained stability diagrams compare very well to recent experimental data [Phys. Rev. B, 84, 245316 (2011)].