Width of the charge-transfer peak in the SU(N) impurity Anderson model and its relevance to non-equilibrium transport

TL;DR

This paper investigates the width of the charge-transfer peak in the SU(N) impurity Anderson model using various computational methods, revealing how it varies with on-site energy and its implications for non-equilibrium transport in quantum dot systems.

Contribution

The study provides a detailed analysis of the charge-transfer peak width in the SU(N) IAM across different regimes, employing DDMRG, NCA, and a variational approach, and discusses experimental relevance.

Findings

For large positive on-site energy, the width equals the resonant level half-width.

For large negative on-site energy, the width scales with N times the half-width.

Variation in the charge-transfer peak affects conductance in quantum dot experiments.

Abstract

We calculate the width $2\Delta_{\text{CT}}$ and intensity of the charge-transfer peak (the one lying at the on-site energy $E_d$) in the impurity spectral density of states as a function of $E_d$ in the SU($N$) impurity Anderson model (IAM). We use the dynamical density-matrix renormalization group (DDMRG) and the noncrossing-approximation (NCA) for $N$=4, and a 1/$N$ variational approximation in the general case. In particular, while for $E_d \gg \Delta$, where $\Delta$ is the resonant level half-width, $\Delta_{\text{CT}}=\Delta$ as expected in the noninteracting case, for $-E_d \gg N \Delta$ one has $\Delta_{\text{CT}}=N\Delta$. In the $N$=2 case, some effects of the variation of $% \Delta_{\text{CT}}$ with $E_d$ were observed in the conductance through a quantum dot connected asymmetrically to conducting leads at finite bias [J. K\"onemann \textit{et al.}, Phys. Rev. B \textbf{73}, 033313 (2006)]. More dramatic effects are expected in similar experiments, that can be carried out in systems of two quantum dots, carbon nanotubes or other, realizing the SU(4) IAM.