Thermoelectric transport through strongly correlated quantum dots

The thermoelectric properties of strongly correlated quantum dots, described by a single-level Anderson model coupled to conduction-electron leads, is investigated using Wilson's numerical renormalization-group method. We calculate the electronic contribution, K₄, to the thermal conductance, the thermopower, S, and the electrical conductance, G, of a quantum dot as a function of both temperature, T, and gate voltage, v₆, for strong, intermediate, and weak Coulomb correlations, U, on the dot. For strong correlations and in the Kondo regime, we find that the thermopower exhibits two sign changes, at temperatures T₁ (v₆) and T₂ (v₆) with T₁T₏ (v₆) T₊ (v₆), where T₏ (v₆) is the position of the Kondo-induced peak in the thermopower, T₊ (v₆) is the Kondo scale, and T₂=O (), where is the level width. The loci of T₁ (v₆) and T₂ (v₆) merge at a critical gate voltage, v₆=v₆^c (U/) beyond which no sign change occurs at finite gate voltage (measured relative to midvalley). We determine v₆^c for different U/ finding that v₆^c coincides, in each case, with entry into the mixed-valence regime. No sign change is found outside the Kondo regime, or, for weak correlations U/1, making such a sign change in S (T) a particularly sensitive signature of strong correlations and Kondo physics. The relevance of this to recent thermopower measurements of Kondo correlated quantum dots is discussed. The results for quantum dots are compared also to the relevant transport coefficients of dilute magnetic impurities in nonmagnetic metals: the electronic contribution, ₄, to the thermal conductivity, the thermopower, S, and the impurity contribution to the electrical resistivity,. In the mixed-valence and empty-orbital regimes, we find, as a function of temperature, two peaks in K₄ as compared to a single peak in ₄, and similarly, G (T) exhibits a finite-temperature peak on entering the mixed-valence regime whereas such a pronounced peak is absent in (T) even far into the empty-orbital regime. We compare and contrast the figure of merit, power factor, and the extent of violation of the Wiedemann-Franz law in quantum dots and dilute magnetic impurities. The extent of temperature scaling in the thermopower and thermal conductance of quantum dots in the Kondo regime is discussed.