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arXiv:2212.10383 · Physical review. B./Physical review. B

Charge Kondo circuit as a detector for electron-electron interactions in a Luttinger liquid

T. K. T. Nguyen, Anton V. Parafilo, H. Q. Nguyen, Mikhail N. Kiselev

Published May 9, 2023• 7 citations
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Abstract

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 $L$ 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 $a$. 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.

DOI
10.1103/physrevb.107.l201402

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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.
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Luttinger-liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter KKK. We suggest a setup to study Luttinger-liquid behavior in quantum wires which allows us to determine KKK from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two KKK's for a single probe would provide strong experimental evidence for the Luttinger-liquid paradigm.
We study the influence of many-body interactions on the transport properties in a two-site charge Kondo circuit recently implemented in a hybrid metal-semiconductor double-quantum dot device [W. Pouse et al., Nat. Phys. 19, 492 (2023)]. There emerge two principal types of interactions: (i) an intrinsic one, described by the Luttinger liquid model, and (ii) an induced one, which appears due to the coupling of the system to an Ohmic environment. Case (i) could be achieved if the charge Kondo circuit operates in the fractional quantum Hall regime, while case (ii) can be implemented via a finite number of open ballistic channels coupled to both the quantum dots. We demonstrate that the conductance scaling for the case of strong and weak interdot coupling is fully determined by the effective interaction parameter, which is the combination of the fractional filling factor $\ensuremath{\nu}=1/m$ and the number of transmitting channels. Furthermore, we predict that the fractional filling factor $\ensuremath{\nu}$ defines a universal Kondo scaling in the vicinity of a special triple-quantum critical point featured by the emergence of a Z3{\mathbb{Z}}_{3}Z3​ parafermion.
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 (gσ=1g_\sigma = 1gσ​=1) and the interaction in the charge sector is repulsive (0<gρ≤10< g_\rho \leq 10<gρ​≤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.
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A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, gc<12{g}_{c}<\frac{1}{2}gc​<21​, and anomalous power laws for 12<gc<1\frac{1}{2}<{g}_{c}<121​<gc​<1, where gc{g}_{c}gc​ is the correlation parameter of the Luttinger liquid. These findings resolve a recent controversy. If elastic potential scattering is present, we find a logarithmically divergent impurity susceptibility at gc<12{g}_{c}<\frac{1}{2}gc​<21​ that can be rationalized in terms of the two-channel Kondo model.