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arXiv:2007.07239 · Physical review. B./Physical review. B

Electric and heat transport in a charge two-channel Kondo device

G.A.R. van Dalum, Andrew K. Mitchell, Lars Fritz

Published Nov 30, 2020• 4 citations
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Abstract

Motivated by the experimental realization of a multi-channel charge Kondo device [Iftikhar et al., Nature (London) 526, 233 (2015)], we study generic charge and heat transport properties of the charge two-channel Kondo model. We present a comprehensive discussion of the out-of-equilibrium and time-dependent charge transport, as well as thermal transport within linear response theory. The transport properties are calculated at, and also in the vicinity of, the exactly solvable Emery-Kivelson point, which has the form of a Majorana fermion resonant level model. We focus on regimes where our solution gives exact results for the physical quantum dot device, and highlight new predictions relevant to future experiments.

DOI
10.1103/physrevb.102.205137

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Motivated by the experimental realization of a multi-channel charge Kondo device [Iftikhar et al., Nature (London) 526, 233 (2015)], we study generic charge and heat transport properties of the charge two-channel Kondo model. We present a comprehensive discussion of the out-of-equilibrium and time-dependent charge transport, as well as thermal transport within linear response theory. The transport properties are calculated at, and also in the vicinity of, the exactly solvable Emery-Kivelson point, which has the form of a Majorana fermion resonant level model. We focus on regimes where our solution gives exact results for the physical quantum dot device, and highlight new predictions relevant to future experiments.
We study a charge two-channel Kondo model, demonstrating that recent experiments [Z. Iftikhar et al, Nature (London) 526, 233 (2015)] realize an essentially perfect quantum simulation-not just of its universal physics, but also nonuniversal effects away from the scaling limit. Numerical renormalization group (RG) calculations yield conductance line shapes encoding RG flow to a critical point involving a free Majorana fermion. By mimicking the experimental protocol, the experimental curve is reproduced quantitatively over 9 orders of magnitude, although we show that far greater bandwidth/temperature separation is required to obtain the universal result. Fermi liquid instabilities are also studied: In particular, our exact analytic results for nonlinear conductance provide predictions away from thermal equilibrium, in the regime of existing experiments.
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.
Quantum dot devices may be tuned to Kondo models which have non-interacting limits such as the Toulouse limit. At sufficiently low temperatures the Toulouse limit can be used to make predictions for charge transport in the devices driven away from equilibrium, e.g. with an ac bias. We investigate non-equilibrium transport in a resonant level model with a single lead which may be mapped onto the Toulouse limit of the one-channel Kondo model. The main results are expressions for the charge current that are exact in the tunnelling couplings, while remaining in the linear response regime of the time-dependent voltage bias. We also show how the line of enquiry directly extends to the tunnelling junction studied by A.~Schiller and S.~Hershfield in which a Kondo impurity interacts separately with two leads.
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 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.