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arXiv:2310.15514

Probing Luttinger Liquid Properties in Multichannel Two-Site Charge Kondo Simulator

Anton V. Parafilo, V. M. Kovalev, Ivan G. Savenko

Published Oct 24, 2023• 0 citations
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Abstract

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 {\it et al.}, Nat. Phys. {\bf 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 $ν=1/m$ and the number of transmitting channels. Furthermore, we predict that the fractional filling factor $ν$ defines a universal Kondo scaling in the vicinity of a special triple quantum critical point featured by the emergence of a $\mathbb{Z}_3$ parafermion.

DOI
10.48550/arxiv.2310.15514

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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 {\it et al.}, Nat. Phys. {\bf 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 ν=1/mν=1/mν=1/m and the number of transmitting channels. Furthermore, we predict that the fractional filling factor ννν defines a universal Kondo scaling in the vicinity of a special triple quantum critical point featured by the emergence of a Z3\mathbb{Z}_3Z3​ parafermion.
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.
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.
Hybrid metal-semiconductor quantum circuits offer a controlled setting for realizing and probing strongly correlated quantum matter. A largely open question that may be addressed by such simulators is whether coupled critical states can combine into new non-Fermi liquid (NFL) phases. Inspired by the recent realization of a two-site charge-Kondo circuit [W. Pouse \textit{et al.}, \href{https://www.nature.com/articles/s41567-022-01905-4}{Nat. Phys. \textbf{19}, 492 (2023)}], we uncover the fate of coupled Kondo anyons emerging from the two-channel-Kondo critical point at each site. Bosonization and quantum Brownian motion methods yield the full quasiballistic phase diagram and low-temperature transport properties, while numerical renormalization group calculations resolve the complementary weak-coupling limit. Together, these provide a unified description, and reveal robust NFL phases with continuously tunable transport and susceptibility exponents. Stronger inter-site coupling ultimately produces a screened Fermi liquid.
Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [W. Pouse et al., Nat. Phys. (2023)NPAHAX1745-247310.1038/s41567-022-01905-4] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here, we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a Z_{3} parafermion emerges at the critical point, characterized by a fractional 1/2ln(3) residual entropy, and scattering fractional charges e/3. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.
We study finite-frequency transport properties of the double dot system recently constructed to observe the two-channel Kondo effect [R. M. Potok et al., Nature 446, 167 (2007)]. We derive an analytical expression for the frequency-dependent linear conductance of this device in the Kondo regime. We show how the features characteristic of the two-channel Kondo quantum critical point emerge in this quantity, which we compute using the results of conformal field theory as well as numerical renormalization group methods. We determine the universal crossover functions describing non-Fermi-liquid vs Fermi-liquid crossovers and also investigate the effects of a finite magnetic field.
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.