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Communications in Physics

Thermopower of a Luttinger-liquid-based Two-channel Charge Kondo Circuit: Nonperturbative Solution

Anton V. Parafilo, T. K. T. Nguyen

Published Feb 21, 2023• 5 citations
Publisher

Abstract

Recently, the influence of electron-electron interactions on the thermoelectric transport in a two-channel charge Kondo circuit has been studied in [Phys. Rev. B 105, L121405 (2022)]. In this paper, we revisit the Luttinger-liquid-based model and discuss in details the limit where the spin field is noninteracting (\(g_\sigma = 1\)) and the interaction in the charge sector is repulsive (\(0< g_\rho \leq 1\)). The thermoelectric transport coefficients are computed nonperturbatively with respect to the reflection amplitude at the quantum point contact. At low temperatures the thermopower shows the non-Fermi liquid behavior in the vicinity of the Coulomb peaks. We also demonstrate that repulsive interaction results in the enhancement of the thermoelectrical power.

DOI
10.15625/0868-3166/17705

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Recently, the influence of electron-electron interactions on the thermoelectric transport in a two-channel charge Kondo circuit has been studied in [Phys. Rev. B 105, L121405 (2022)]. In this paper, we revisit the Luttinger-liquid-based model and discuss in details the limit where the spin field is noninteracting ((g_\sigma = 1)) and the interaction in the charge sector is repulsive ((0< g_\rho \leq 1)). The thermoelectric transport coefficients are computed nonperturbatively with respect to the reflection amplitude at the quantum point contact. At low temperatures the thermopower shows the non-Fermi liquid behavior in the vicinity of the Coulomb peaks. We also demonstrate that repulsive interaction results in the enhancement of the thermoelectrical power.
In this Letter we investigate the properties of a quantum impurity model in the presence of additional many-body interactions between mobile carriers. The fundamental question which is addressed here is how the interactions in the charge and spin sectors of an itinerant system affect the quantum impurity physics in the vicinity of the intermediate coupling fixed point. To illustrate the general answer to this question we discuss a two-channel charge Kondo circuit model. We show that the electron-electron interactions resulting in the formation of a massive spin mode in an itinerant electron subset drive the system away from the unstable non-Fermi-liquid (NFL) fixed point to the stable Fermi-liquid (FL) regime. We discuss the thermoelectric response as a benchmark for the NFL-FL crossover.
We theoretically investigate the thermoelectric transport through a circuit implementation of the three-channel charge Kondo model quantum simulator [Z. Iftikhar et al., Science 360, 1315 (2018)SCIEAS0036-807510.1126/science.aan5592]. The universal temperature scaling law of the Seebeck coefficient is computed perturbatively approaching the non-Fermi liquid strong coupling fixed point using the Abelian bosonization technique. The predicted T^{1/3}logT scaling behavior of the thermoelectric power sheds light on the properties of Z_{3} emerging parafermions and gives access to exploring prefractionalized zero modes in the quantum transport experiments. We discuss a generalization of approach for investigating a multichannel Kondo problem with emergent Z_{N}→Z_{M} crossovers between "weak" non-Fermi liquid regimes corresponding to different low-temperature fixed points.
We investigate the effects of the electron-electron interactions on the quantum transport through a charge Kondo circuit. The setup consists of a quantum dot sandwiched between two leads by two nearly transparent single mode quantum point contacts. The size of the interacting area LLL in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot aaa. We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.
The thermopower of a Luttinger liquid (LL), originating from the energy dispersion of electrons at the Fermi level and/or from the backscattering of electrons by impurities, is analytically evaluated. It is shown that in both cases the thermopower is described by a corresponding Fermi-liquid formula renormalized by an interaction-dependent factor. For an infinite LL the renormalization coefficients decrease with an increase of the electron-electron interaction. In a realistic situation, when a LL wire is connected to leads of noninteracting electrons, the dispersion-induced thermopower in the limit of strong repulsive interaction is strongly suppressed, ${S}_{W}^{(d)}\ensuremath{\sim}{g}^{2}{S}_{0}^{(d)}\ensuremath{\ll}{S}_{0}^{(d)}$ (here S0(d){S}_{0}^{(d)}S0(d)​ is the corresponding Fermi-liquid value for the thermopower and $g\ensuremath{\ll}1$ is the LL correlation parameter), while the impurity-induced thermopower ${S}_{W}^{(i)}\ensuremath{\sim}{S}_{0}^{(i)}/g$ is enhanced by the interelectron interaction.
Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant K=1/2K = 1/2K=1/2: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport
We investigate thermoelectric and thermodynamic properties of a Tomonaga-Luttinger liquid with interaction parameter K=1/2K=1/2K=1/2 in the presence of a localized impurity. Using bosonization and refermionization, we derive an exact expression for the thermopower in the nonlinear regime and obtain the corresponding Seebeck coefficient in linear response. At low temperature, the Seebeck coefficient follows a Mott-like relation governed by the energy dependence of the transmission coefficient and is found to be closely related to the entropy per particle. This connection allows us to derive using Kelvin formula the thermopower contribution to the entropy density variation and the charge-carriers contribution to the heat capacity density. Both quantities exhibit Mott-like behavior in the low-temperature regime. We apply our results to a fractional quantum Hall quantum point contact and to a one-channel quantum conductor coupled to an Ohmic environment. Our results demonstrate the close connection between thermoelectric transport and thermodynamic properties in interacting one-dimensional quantum systems.
We develop a conformal field theory approach for investigation of the quantum charge, heat, and thermoelectric transport through a quantum impurity fine-tuned to a non-Fermi liquid regime. The non-Fermi-liquid operational mode is associated with the overscreened spin Kondo effect and controlled by the number of orbital channels. The universal low-temperature scaling and critical exponents for Seebeck and Peltier coefficients are investigated for the multichannel geometry. We discuss the universality of Lorenz ratio and power factor beyond the Fermi-liquid paradigm. Different methods of verifying our findings based on the recent experiments are proposed.