Numerical renormalization group approach to a quartet quantum-dot array connected to reservoirs:gate-voltage dependence of the conductance

Abstract

The ground-state properties of quartet quantum-dot arrays are studied using the numerical renormalization group (NRG) method with a four-site Hubbard model connected to two non-interacting leads. Specifically, we calculate the conductance and local charge in the dots from the many-body phase shifts, which can be deduced from the fixed-point eigenvalues of NRG. As a function of the on-site energy ${\epsilon }_d$ which corresponds to the gate voltage, the conductance shows alternatively wide peak and valley. Simultaneously, the total number of electrons $N_{\mathrm{el}}$ in the four dots shows a quantized stair case behavior due to a large Coulomb interaction $U$. The conductance plateaus of the Unitary limit emerging for odd $N_{\mathrm{el}}$ are caused by the Kondo effect. The valleys of the conductance emerge for even $N_{\mathrm{el}}$, and their width becomes substantially large at half-filling. It can be regarded as a kind of the Mott-Hubbard insulating behavior manifesting in a small system. These structures of the plateaus and valleys become weak for large values of the hybridization strength $\Gamma$ between the chain and leads. We also discuss the parallel conductance for the array connected to four leads.

8 pages, 9 figures

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