Fano-Kondo effect in side-coupled double quantum dots at fin ite temperatures and the importance of the two-stage Kondo screening Rok ˇ Zitko 1 $^{1}$Joˇzef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slo venia (Dated: November 1, 2018) We study the zero-bias conductance through the system of two quantum dots, one of which is embedded directly between the source and drain electrodes, while the second dot is side-coupled to the first one through a tunneling junction. Modeling the system using the two-impurity Anderson model, we compute the temperature- dependence of the conductance in various parameter regimes using the numerical renormalization group. We consider the non-interacting case, where we study the extent of the departure from the conventional Fano reso- nance line shape at finite temperatures, and the case where th e embedded and/or the side-coupled quantum dot is interacting, where we study the consequences of the coexistence of the Kondo and Fano effects. If the side- coupled dot is very weakly interacting, the occupancy changes by two when the on-site energy crosses the Fermi level and a Fano-resonance-like shape is observed. If the interaction on the side-coupled dot is sizeable, the oc- cupancy changes only by one and a very different line-shape results, which is strongly and characteristically temperature dependent. These results suggest an intriguing alternative interpretation of the recent experimental results study of the transport properties of the side-coupled double quantum dot [Sasaki et al., Phys. Rev. Lett. 103, 266806 (2009)]: the observed Fano-like conductance anti-resonance may, in fact, result from the two-stage Kondo effect in the regime where the experimental temperature is between the higher and the lower Kondo temperature. PACS numbers: 72.15.Qm, 75.20.Hr, 73.23.-b, 73.40.Gk, 73.63.Kv In condensed-matter physics, the Fano resonance line shape 1,2 is commonly observed in the low-temperature zero- bias conductance curves of various mesoscopic and nanoscale electronic devices when the energy of a weakly coupled dis- crete state is swept across the Fermi level using gate voltages. A prototype system where Fano physics may be observed consists of a single quantum dot side-coupled to a quantum wire 3–15 . The Fano line shape results from an interference of the quantum amplitudes for the conduction pathway directly through the quantum wire without passing through the quan- tum dot and the indirect conduction pathway via the quantum dot. The first pathway plays the role of a broad background process, while the second corresponds to a resonant scattering channel. The conductance as a function of the discrete state energy level ϵ is well described by the Fano function The situation becomes more involved in a related structure consisting of two quantum dots, the first of which is embed- ded in the direct conduction pathway between the source and drain electrodes and the second is side-coupled to the first one by weak tunnel coupling, as illustrated in Fig. 1. This nanostructure, also known as the “side-coupled double quan - tum dot”, allows to study the interference between the direc t and indirect conduction pathways (i.e., the Fano effect), as well as various correlation effects resulting from the strong electron-electron repulsion between the confined electron s, in particular the Kondo effect 16–23 . Taking into account only the electron levels in close vicinity of the Fermi level, this system can be adequately described at low temperatures us- ing a two-impurity Anderson model which is a simple ex- tension of the single-impurity model that is commonly used for studying transport properties of single ultra-small quan- tum dots$^{24}$. The side-coupled double quantum dots have been intensively studied theoretically 25–33 , uncovering a fascinating interplay between many-particle effects and quantum interfer- ence, however the first experimental study of this system has been performed only very recently (Ref. 34). Most previous is a dimensionless energy that measures the energy difference from a resonance energy ϵ r in units of the resonance half- width Γ , q is the Fano parameter given by the ratio of reso- nant and background scattering amplitudes, while a and b are some coefficients. 74 This energy dependence holds as long as the background conductance is constant over the width of the resonance; in experiments, curve fitting with Fano profile is typically done in an energy window of the order of several times Γ . where arXiv:1001.1983v2[cond-mat.mes-hall]4 Mar 2010 I. INTRODUCTION Figure 1: (Color online) Schematic representation of the double quantum dot nanostructure consisting of a quantum dot (d), em- bedded between the source and drain electrodes, and a side-coupled quantum dot (a). source drain d a V V t G ( E ) = a ( E + q ) 2 1 + E 2 + b, (1) E = ϵ − ϵ r Γ (2)