An equation of motion analysis of the two stage Kondo effect in T-shaped double-quantum-dot systems

Author-Highlights
• The Anderson model is used in connection with the T-shaped double-quantum-dot system.
• We include terms beyond Hartree–Fock approximation for the equation of motion method.
• We evaluate the first stage Kondo temperature in the strong Coulomb interaction limit.

We use the equation of motion method in connection with a generalized Anderson Hamiltonian to evaluate the electronic transmission in a T-shaped double quantum dot system. We consider the strong Coulomb interaction regime (U1→∞U1→∞, U2→∞U2→∞) using a decoupling procedure that includes terms beyond the standard Hartree–Fock approximation. The typical manifestation of the two stage Kondo effect is reflected in system's electronic transmission coefficient that presents both a large Lorentzian and a sharp dip around ω=0ω=0. We provide an analytical result for the first stage Kondo temperature that includes corrections due to the presence of an additional quantum dot in the system. For the second stage Kondo effect, we identify the logarithmic correction that is responsible for the additional dip in the system's electronic transmission coefficient.