Z_{3} Parafermion in the Double Charge Kondo Model.

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.

Two-Channel Charge-Kondo Physics in Graphene Quantum Dots.

Nanoelectronic quantum dot devices exploiting the charge-Kondo paradigm have been established as versatile and accurate analogue quantum simulators of fundamental quantum impurity models. In particular, hybrid metal-semiconductor dots connected to two metallic leads realize the two-channel Kondo (2CK) model, in which Kondo screening of the dot charge pseudospin is frustrated. In this article, a two-channel charge-Kondo device made instead from graphene components is considered, realizing a pseudogapped version of the 2CK model. The model is solved using Wilson's Numerical Renormalization Group method, uncovering a rich phase diagram as a function of dot-lead coupling strength, channel asymmetry, and potential scattering. The complex physics of this system is explored through its thermodynamic properties, scattering T-matrix, and experimentally measurable conductance. The strong coupling pseudogap Kondo phase is found to persist in the channel-asymmetric two-channel context, while in the channel-symmetric case, frustration results in a novel quantum phase transition. Remarkably, despite the vanishing density of states in the graphene leads at low energies, a finite linear conductance is found at zero temperature at the frustrated critical point, which is of a non-Fermi liquid type. Our results suggest that the graphene charge-Kondo platform offers a unique possibility to access multichannel pseudogap Kondo physics.

Fractional Entropy of Multichannel Kondo Systems from Conductance-Charge Relations.

Fractional entropy is a signature of nonlocal degrees of freedom, such as Majorana zero modes or more exotic non-Abelian anyons. Although direct experimental measurements remain challenging, Maxwell relations provide an indirect route to the entropy through charge measurements. Here we consider multichannel charge-Kondo systems, which are predicted to host exotic quasiparticles due to a frustration of Kondo screening at low temperatures. In the absence of experimental data for the charge occupation, we derive relations connecting the latter to the conductance, for which experimental results have recently been obtained. Our analysis indicates that Majorana and Fibonacci anyon quasiparticles are well developed in existing two- and three-channel charge-Kondo devices, and that their characteristic k_{B}logsqrt[2] and k_{B}log[(1+sqrt[5])/2] entropies are experimentally measurable.

SO(5) Non-Fermi Liquid in a Coulomb Box Device.

Non-Fermi liquid (NFL) physics can be realized in quantum dot devices where competing interactions frustrate the exact screening of dot spin or charge degrees of freedom. We show that a standard nanodevice architecture, involving a dot coupled to both a quantum box and metallic leads, can host an exotic SO(5) symmetry Kondo effect, with entangled dot and box charge and spin. This NFL state is surprisingly robust to breaking channel and spin symmetry, but destabilized by particle-hole asymmetry. By tuning gate voltages, the SO(5) state evolves continuously to a spin and then "flavor" two-channel Kondo state. The expected experimental conductance signatures are highlighted.

Enhanced photocatalysis and biomolecular sensing with field-activated nanotube-nanoparticle templates.

The development of new catalysts for oxidation reactions is of central importance for many industrial processes. Plasmonic catalysis involves photoexcitation of templates/chips to drive and enhance oxidation of target molecules. Raman-based sensing of target molecules can also be enhanced by these templates. This provides motivation for the rational design, characterization, and experimental demonstration of effective template nanostructures. In this paper, we report on a template comprising silver nanoparticles on aligned peptide nanotubes, contacted with a microfabricated chip in a dry environment. Efficient plasmonic catalysis for oxidation of molecules such as p-aminothiophenol results from facile trans-template charge transfer, activated and controlled by application of an electric field. Raman detection of biomolecules such as glucose and nucleobases are also dramatically enhanced by the template. A reduced quantum mechanical model is formulated, comprising a minimum description of key components. Calculated nanotube-metal-molecule charge transfer is used to understand the catalytic mechanism and shows this system is well-optimized.

Kondo blockade due to quantum interference in single-molecule junctions.

Molecular electronics offers unique scientific and technological possibilities, resulting from both the nanometre scale of the devices and their reproducible chemical complexity. Two fundamental yet different effects, with no classical analogue, have been demonstrated experimentally in single-molecule junctions: quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Here we unify these phenomena, showing that transport through a spin-degenerate molecule can be either enhanced or blocked by Kondo correlations, depending on molecular structure, contacting geometry and applied gate voltages. An exact framework is developed, in terms of which the quantum interference properties of interacting molecular junctions can be systematically studied and understood. We prove that an exact Kondo-mediated conductance node results from destructive interference in exchange-cotunneling. Nonstandard temperature dependences and gate-tunable conductance peaks/nodes are demonstrated for prototypical molecular junctions, illustrating the intricate interplay of quantum effects beyond the single-orbital paradigm.

Kondo Impurities in the Kitaev Spin Liquid: Numerical Renormalization Group Solution and Gauge-Flux-Driven Screening.

Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.

Local moment formation and Kondo screening in impurity trimers.

We study theoretically a triangular cluster of three magnetic impurities, hybridizing locally with conduction electrons of a metallic host. Such a cluster is the simplest to exhibit frustration, an important generic feature of many complex molecular systems in which different interactions compete. Here, low-energy doublet states of the trimer are favored by effective exchange interactions produced by strong electronic repulsion in localized impurity orbitals. Parity symmetry protects a level crossing of such states on tuning microscopic parameters, while an avoided crossing arises in the general distorted case. Upon coupling to a metallic host, the behavior is shown to be immensely rich because collective quantum many-body effects now also compete. In particular, impurity degrees of freedom are totally screened at low temperatures in a Kondo-screened Fermi liquid phase, while degenerate ground states persist in a local moment phase. Local frustration drives the quantum phase transition between the two, which may be first order or of Kosterlitz-Thouless type, depending on symmetries. Unusual mechanisms for local moment formation and Kondo screening are found due to the orbital structure of the impurity trimer. Our results are of relevance for triple quantum dot devices. The problem is studied by a combination of analytical arguments and the numerical renormalization group.

Two-channel Kondo physics in two-impurity Kondo models.

We consider the non-Fermi-liquid quantum critical state of the spin-S two-impurity Kondo model and its potential realization in a quantum dot device. Using conformal field theory and the numerical renormalization group, we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin S. Distinct conductance signatures are shown to arise as a function of device asymmetry, with the square-root behavior commonly believed to arise at low-energies dominant only in certain regimes.

Exact crossover Green function in the two-channel and two-impurity Kondo models.

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.