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Left: Schematic representation of parallel double quantum dots (DQ1 and DQ2) connected to two left (L) and right (R) leads by equal tunneling matrix elements t α i. Right: Schematic representation of a configuration of parallel quantum dots, symmetrically coupled to the leads, obtained as a result of the transformation (5). The vertical up-down arrow indicates the presence of two-particle interactions between quantum dots (see Eq. 17 in the Section IV A of the paper).
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We propose a version of functional renormalization-group (fRG) approach, which is, due to including Litim-type cutoff and switching off (or reducing) the magnetic field during fRG flow, capable describing singular Fermi liquid (SFL) phase, formed due to presence of local moments in quantum dot structures. The proposed scheme allows to describe the...
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... parallel quantum dots connected to two conduct- ing leads (see Fig. 1) can be modelled by the Hamilto- nian [30] ...
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Citations
... Similarly to Ref. [57] we have found that the convergence of the vertices obtained from fRG equations can be achieved by applying the counterterm technique. The counterterm (which corresponds in our case to introducing auxiliary magnetic fieldh = 1.5t, switched off linearly with Λ starting from the scale Λ c = 0.1t) allows us continuing the S st (U/t) dependence beyond the point at which the fRG approach without the counterterm breaks down, see Fig. 2. ...
We investigate magnetic, charge and transport properties of hexagonal graphene nanoflakes (GNFs) connected to two metallic leads by using the functional renormalization group (fRG) method. The interplay between the on-site and long-range interactions leads to a competition of semimetal (SM), spin density wave (SDW), and charge-density-wave (CDW) phases. The ground-state phase diagrams are presented for the GNF systems with screened realistic long-range electron interaction [T. O. Wehling, et. al., Phys. Rev. Lett. {\bf 106}, 236805 (2011)], as well as uniformly screened long-range Coulomb potential \propto 1/r. We demonstrate that the realistic screening of Coulomb interaction by $\sigma$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential. This enhancement gives rise to a wide region of stability of the SM phase for realistic interaction,
such that freely suspended GNFs are far from both SM-SDW and SM-CDW phase-transition boundaries and correspond to the SM phase.
Close relation between the linear conductance and the magnetic or charge states of the systems is discussed. A comparison of the results with those of other studies on GNFs systems and infinite graphene sheet is presented.
... Even in the presence of the Coulomb interaction, this state remains weakly coupled to the leads in the vicinity of half filling ( j = 0), and the local moment is not destroyed [31]. In this respect, the QQD system is similar to the double quantum dot system, where the presence of the odd, weakly hybridized with the leads, state provides the possibility for formation of a correlation induced local magnetic moment in the system [13,16,30,31]. ...
... In the present study we consider only the flow of the self-energy and neglect the frequency dependence of the self-energy and the flow of the two-particle and higher order vertex functions. It was shown that neglecting frequency dependence of the self-energy allows to describe both, equilibrium [41] and non-equilibrium properties [43,44], as well as to access the SFL state [30,31]. On the other hand, neglecting flow of two-particle and higher order vertices allows us to fulfill exactly charge conservation, which is typically violated in higher order truncations. ...
... To induce small initial spin splitting, which can be further enhanced by correlation effects during fRG flow (and therefore allows us to obtain local moments), we apply small magnetic field H/max(Γ L,R ) = 0.001. Due to use of truncation (8) of fRG hierarchy at first (self-energy) instead or second order (vertices), the counterterm technique, suggested in previous studies [30,31] is not necessary, and does not change the obtained results. ...
We apply the non-equilibrium functional renormalization group approach treating flow of the electronic self-energies, to describe local magnetic moments formation and electronic transport in a quadruple quantum dot (QQD) ring, coupled to leads, with moderate Coulomb interaction on the quantum dots. We find that at zero temperature depending on parameters of the QQD system the regimes with zero, one, or two almost local magnetic moments in the ring can be realized, and the results of the considered approach in equilibrium agree qualitatively with those of more sophisticated fRG approach treating also flow of the vertices. It is shown that the almost formed local magnetic moments, which exist in the equilibrium, remain stable in a wide range of bias voltages near equilibrium. The destruction of the local magnetic moments with increasing bias voltage is realized in one or two stages, depending on the parameters of the system; for two-stage process the intermediate phase possesses fractional magnetic moment. We present zero-temperature results for current-voltage dependences and differential conductances of the system, which exhibit sharp features at the transition points between different magnetic states. The occurrence of interaction induced negative differential conductance phenomenon is demonstrated and discussed. For one local moment in the ring and finite hopping between the opposite quantum dots, connected to the leads, we find suppression of the conductance for one of the spin projections in infinitesimally small magnetic field, which occurs due to destructive interference of different electron propagation paths and can be used in spintronic devices.
... In particular, in the simplest ring geometry of the system, consisting of two quantum dots coupled in parallel to two common leads, the appearance of the phase transition to the SFL state is related to the specific electron redistribution between the even and odd states. For the parallel quantum dot system with all hopping parameters between dots and leads equal, the SFL state has been studied by various methods [31,32] and was shown to appear due to the full decoupling of the odd state from the leads, which yields formation of the local magnetic moment in the system. ...
... 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]. ...
... Method. To treat the effects of two particle interaction U , we use the one-particle irreducible (1PI) version of the fRG method [53], supplemented by the counterterm, recently introduced in Ref. [32], which allows for treatment of local moments. This method starts with considering the non-interacting propagator of quantum dot system, obtained by projection of the leads and taking the wideband limit [25,59,60], as a matrix in the quantum dot space [25], ...
We explore the effects of asymmetry of hopping parameters between double parallel quantum dots and the leads on the conductance and a possibility of local magnetic moment formation in this system using functional renormalization group approach with the counterterm. We demonstrate a possibility of a quantum phase transition to a local moment regime (so called singular Fermi liquid (SFL) state) for various types of hopping asymmetries and discuss respective gate voltage dependences of the conductance. It is shown, that depending on the type of the asymmetry, the system can demonstrate either a first order quantum phase transition to SFL state, accompanied by a discontinuous change of the conductance, similarly to the symmetric case, or the second order quantum phase transition, in which the conductance is continuous and exhibits Fano-type asymmetric resonance near the transition point. A semi-analytical explanation of these different types of conductance behavior is presented.
