Conductance scaling in Kondo-correlated quantum dots: Role of level asymmetry and charging energy

Abstract

The low-temperature electrical conductance through correlated quantum dots provides a sensitive probe of the physics (e.g., of Fermi-liquid versus non-Fermi-liquid behavior) of such systems. Here, we investigate the role of level asymmetry (gate voltage) and local Coulomb repulsion (charging energy) on the low-temperature and low-field scaling properties of the linear conductance of a quantum dot described by the single-level Anderson impurity model. We use the numerical renormalization group to quantify the regime of gate voltages and charging energies where universal Kondo scaling may be observed and also quantify the deviations from this universal behavior with increasing gate voltage away from the Kondo regime and with decreasing charging energy. We also compare our results with those from a recently developed method for linear and nonlinear transport, which is based on renormalized perturbation theory using dual fermions, finding excellent agreement at particle-hole symmetry and for all charging energies and reasonable agreement at small finite level asymmetry. Our results could be a useful guide for detailed experiments on conductance scaling in semiconductor and molecular quantum dots exhibiting the Kondo effect.

Local susceptibility and Kondo scaling in the presence of finite bandwidth

“…Given = 4 together with E tr = 40, these results are considered well converged (see figure caption on the convergence of T 1/2 /T sc K with NRG parameters). Finally, note that the value for T 1/2 /T sc K above also agrees well with the one cited by Merker et al [10], which in the wide-band limit suggests T 1/2 /T sc K 1.04. Overall, with T 1/2 /T sc K being constant, this is fully consistent with the fact that T 1/2 itself may serve and is frequently used as a universal definition of T K , with a minor constant proportionality factor of 1.03 to the T sc K used here.…”

“…The above results have direct implications on the Fermi liquid coefficients derived from the conductance g(T ). For example, with the Fermi liquid coefficient c T defined by [7][8][9][10], this strongly depends on the precise definition of T K . Note that even though T K is apparently well defined through the magnetic susceptibility, depending on the precise definition of the latter, nevertheless, variations of up to 10% are seen in the ratio T d K /T sc K within a well-defined Kondo regime [cf.…”

“…(4) as the relevant Kondo temperature for universal scaling. Specifically, one obtains (11) with c T ≡ π 4 16 the well-known Fermi-liquid coefficient with respect to temperature for Kondo impurities [7][8][9][10].…”

Transport properties of fully screened Kondo models

“…We note that while the scale T K obviously depends on the truncation, the ratios of the (in principle) observable scales T * K /T 0 and T * K /T * * K also depend on it, i.e., the truncated RTRG equations are not able to yield reliable results for these quantities. For example, for the spin-1/2 model we find in second and third order T * K /T 0 = 1.15 and T * K /T 0 = 0.52, respectively, while recent numerical RG calculations [93,94] give T * K /T 0 ≈ 1.04 in the Kondo limit of the single-impurity Anderson model.…”

Analysis of low-energy response and possible emergent SU(4) Kondo state in a double quantum dot

“…We first of all test this approximation for the temperature dependence of conductance against the NRG results in Fig. 2 in the paper by Merker et al 36 for the single impurity Anderson model. The results of this comparison are shown in Fig.…”