Thermoelectric transport through strongly correlated quantum dots

Abstract

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, K e , 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, v g , 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 T 1 ͑v g ͒ and T 2 ͑v g ͒ with T 1 Ͻ T 2 . We find that T 1 Ͼ T p ͑v g ͒ϷT K ͑v g ͒, where T p ͑v g ͒ is the position of the Kondo-induced peak in the thermopower, T K ͑v g ͒ is the Kondo scale, and T 2 = O͑⌫͒, where ⌫ is the level width. The loci of T 1 ͑v g ͒ and T 2 ͑v g ͒ merge at a critical gate voltage, v g = v g c ͑U / ⌫͒ beyond which no sign change occurs at finite gate voltage ͑measured relative to midvalley͒. We determine v g c for different U / ⌫ finding that v g 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 / ⌫Շ1, making such a sign change in S͑T͒ 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, e , 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 K e as compared to a single peak in e , and similarly, G͑T͒ exhibits a finite-temperature peak on entering the mixed-valence regime whereas such a pronounced peak is absent in ͑T͒ 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.

Transient thermoelectricity in a vibrating quantum dot in Kondo regime

“…Subsequently, steady state thermopower curve is nonmonotonic and goes to zero at T =0 eventually. This issue has been confirmed by other sources too 19 . On the other hand, the Kondo resonance is simply nonexistent when the dot is in its initial level since T≫ T K .…”

Thermoelectric properties of a weakly coupled quantum dot: enhanced thermoelectric efficiency

“…Also, recently it has been reported that deviations from the WiedemannFranz law lead to enhancement of ZT in nanocontacts made of two-capped single wall nanotubes [24], quantum dots attached to ferromagnetic leads [18], and strongly correlated quantum dots [25]. The maximization of S 2 GT , discussed earlier, has a direct impact on the dimensionless figure of merit ZT when the phonon contribution to the thermal conductance is ignored…”

Thermoelectric energy harvesting with quantum dots

“…[19]. Two-terminal geometries using mesoscopic conductors have been considered, notably using quantum dots [5,20,21,7,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. In the two-terminal geometry, both temperature and voltage bias are applied to the sample and the thermoelectric response is investigated.…”