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.
Highlights
The discovery of the Kondo effect[1] in semiconducting quantum dots (QDs),[2,3,4,5,6,7,8,9,10] has spurred the study of electronic transport through QDs
Several physical effects are generically observed when the system is cooled at cryogenic temperatures due to the large Coulomb repulsion in these nanoscopic QDs, such as Coulomb blockade and the Kondo effect, which implies a resonance at the Fermi energy in the spectral density of the dot state, that leads to an anomalous peak in the differential conductance G(V ) = dI/dV at zero bias voltage V, where I is the current through the QD
We have calculated the width of the charge transfer peak in the infinite-U SU(4) Anderson model as a function of the impurity level Ed and for the general SU(N ) case in the Kondo regime −Ed ≫ N ∆, where ∆ is half the resonant level width
Summary
The discovery of the Kondo effect[1] in semiconducting quantum dots (QDs),[2,3,4,5,6,7,8,9,10] has spurred the study of electronic transport through QDs. Semiconducting QDs are characterized by the enormous possibilities for tuning the different parameters In all these systems, several physical effects are generically observed when the system is cooled at cryogenic temperatures due to the large Coulomb repulsion in these nanoscopic QDs, such as Coulomb blockade and the Kondo effect, which implies a resonance at the Fermi energy in the spectral density of the dot state, that leads to an anomalous peak in the differential conductance G(V ) = dI/dV at zero bias voltage V , where I is the current through the QD.
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