Spectral density of an interacting dot coupled indirectly to conducting leads

Abstract

We study the spectral density of electrons ρ dσ (ω) in an interacting quantum dot (QD) with a hybridization λ to a non-interacting QD, which in turn is coupled to a non-interacting conduction band. The system corresponds to an impurity Anderson model in which the conduction band has a Lorentzian density of states of width ∆2. We solved the model using perturbation theory in the Coulomb repulsion U (PTU) up to second order and a slave-boson mean-field approximation (SBMFA). The PTU works surprisingly well near the exactly solvable limit ∆2 −→ 0. For fixed U and large enough λ or small enough ∆2, the Kondo peak in ρ dσ (ω) splits into two peaks. This splitting can be understood in terms of weakly interacting quasiparticles. Before the splitting takes place the universal properties of the model in the Kondo regime are lost. Using the SBMFA, simple analytical expressions for the occurrence of split peaks are obtained. For small or moderate ∆2, the side bands of ρ dσ (ω) have the form of narrow resonances, that were missed in previous studies using the numerical renormalization group. This technique also has shortcomings for describing properly the split Kondo peaks. As the temperature is increased, the intensity of the split Kondo peaks decreases, but it is not completely suppressed at high temperatures.

Zero-field splitting of the Kondo resonance and quantum criticality in triple quantum dots

“…25,44 For this to happen, the QD connected to the leads must be essentially a resonant non-interacting level, while the "side dot" is set within the Kondo regime. Although the splitting of the ASR can be interpreted here as a result of interference between single-particle and Kondo resonances, 45 a more subtle explanation points towards a manifestation of the Friedel sum rule. 46 In general, this implies that the zero-temperature impurity's spectral function A 11 (ω, T = 0) evaluated at the Fermi level, must satisfy the condition: 25,44 where φ is a phase shift due to a structured hybridization function ∆(ω) and n 1 is the average of the impurity's number operator.…”

Ferromagnets-induced splitting of molecular states of T-shaped double quantum dots

“…Since the only nonquadratic terms in the Hamiltonian are related to the Coulomb interactions, the subsystem containing F and QD1 can now be diagonalized exactly. The whole model is then equivalent to the Anderson impurity (corresponding to QD2) coupled to the lead possessing Lorentzian density of states (corresponding to the diagonalized subsystem containing F and QD1) [24]. Then, treating t perturbatively to the second order and defining Δε ex QD2 to be the difference between the shifts of different spins for the singly occupied QD2, we obtain [14] where (14) is not trivial.…”

Perfect spin polarization in T-shaped double quantum dots due to the spin-dependent Fano effect

“…3, such splitting is absent. 39 The observed splitting is exclusively due to the presence of the exchange field.…”

“…We also note that in general the splitting of the Kondo peak can also occur in the case of relatively large hopping between the dots. [38][39][40] However, for parameters assumed in Fig. 3, such splitting is absent.…”

“…We note that in the case of a noninteracting first dot, the model corresponds to the single-impurity Anderson model with nonconstant density of states. At low temperatures, one should then expect a single-stage Kondo effect to occur 20,[35][36][37][38][39][40] . However, due to the presence of the exchange field, the Kondo resonance becomes suppressed, which happens once |∆ε (2) exch | T K , where T K is the Kondo temperature.…”