Functional renormalization group approach to transport through correlated quantum dots

Abstract

We investigate the effect of local Coulomb correlations on electronic transport through a variety of coupled quantum dot systems connected to Fermi liquid leads. We use a newly developed functional renormalization group scheme to compute the gate voltage dependence of the linear conductance, the transmission phase, and the dot occupancies. A detailed derivation of the flow equations for the dot level positions, the inter-dot hybridizations, and the effective interaction is presented. For specific setups and parameter sets we compare the results to existing accurate numerical renormalization group data. This shows that our approach covers the essential physics and is quantitatively correct up to fairly large Coulomb interactions while being much faster, very flexible, and simple to implement. We then demonstrate the power of our method to uncover interesting new physics. In several dots coupled in series the combined effect of correlations and asymmetry leads to a vanishing of transmission resonances. In contrast, for a parallel double-dot we find parameter regimes in which the two-particle interaction generates additional resonances.

Josephson current through a single Anderson impurity coupled to BCS leads

“…The truncated fRG was demonstrated to successfully describe strong correlation effects (such as important aspects of Kondo physics). 26 At zero temperature, the approximate flow equations for Σ Λ := −γ Λ 1 and Γ Λ := γ Λ 2 explicitly read (a detailed derivation can be found in Ref. 42)…”

“…zerofrequency) transport properties of multi-level quantum dot geometries connected to Fermi liquid leads up to fairly large U . 26,27 In this paper we establish the accuracy of fRG in treating the Josephson problem by comparing with analytical results at ∆ = ∞ as well as with our NRG data.…”

Functional renormalization group study of parallel double quantum dots: Effects of asymmetric dot-lead couplings

“…The essential feature of these effects is appearance of resonance peak structures in the conductance, making electronic transport properties very sensitive to small changes of parameters, which may be important for practical applications. In this context, the interplay and cooperation between the correlation effects and quantum interference, associated with a system geometry, can be significantly important and provide unexpected electron transport features [24][25][26][27][28].…”

“…Although this method was adapted to study quantum dot systems, including fairly complex geometries, long time ago [17,24,25,58], only recently its modification, allowing to describe SFL state and providing a good agreement with the numerical renormalization group data for parallel quantum dot system up to the intermediate value of the interaction, was proposed [32].…”

Non-Markovian decoherence theory for a double-dot charge qubit

“…Stavrou and Hu [14] considered in details the wavefunctions of the double dot charge qubit for decoherence analysis. Karrasch, et al come with the functional renormalization group approach in dealing with the transport aspects of the multiple coupled dots [15]. The non-Markovian dynamics has also recently been studied by a suitable spin-boson model considering the acoustic phonons by Thorwart, et al using numerical quasiadiabatic propagator path integral scheme [16,17].…”