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

TL;DR

This paper investigates the conductance and charge properties of a quartet quantum-dot array connected to leads, revealing gate-voltage-dependent conductance peaks, Coulomb blockade, Kondo effects, and Mott-Hubbard insulating behavior using the numerical renormalization group method.

Contribution

The study applies the NRG method to a four-site Hubbard model to analyze conductance and charge quantization in a quantum-dot array, highlighting the interplay of Kondo and Mott-Hubbard phenomena.

Findings

Conductance exhibits alternating peaks and valleys as a function of gate voltage.

Quantized electron number in dots shows staircase behavior due to Coulomb interaction.

Kondo effect causes conductance plateaus at odd electron numbers.

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 $N_{\rm el}$ 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 $N_{\rm el}$ are caused by the Kondo effect. The valleys of the conductance emerge for even $N_{\rm el}$, 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.