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arXiv:cond-mat/0602218 · Europhysics Letters (EPL)

Enhanced two-channel Kondo physics in a quantum box device

Paata Kakashvili, Henrik Johannesson

Published Jul 19, 2007• 6 citations
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Abstract

We propose a design for a one-dimensional quantum box device where the charge fluctuations are described by an anisotropic two-channel Kondo model. The device consists of a quantum box in the Coulomb blockade regime, weakly coupled to a quantum wire by a single-mode point contact. The electron correlations in the wire produce strong backscattering at the contact, significantly increasing the Kondo temperature as compared to the case of non-interacting electrons. By employing boundary conformal field theory techniques we show that the differential capacitance of the box exhibits manifest two-channel Kondo scaling with temperature and gate voltage, uncontaminated by the one-dimensional electron correlations. We discuss the prospect to experimentally access the Kondo regime with this type of device.

DOI
10.1209/0295-5075/79/47004

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We propose a design for a one-dimensional quantum box device where the charge fluctuations are described by an anisotropic two-channel Kondo model. The device consists of a quantum box in the Coulomb blockade regime, weakly coupled to a quantum wire by a single-mode point contact. The electron correlations in the wire produce strong backscattering at the contact, significantly increasing the Kondo temperature as compared to the case of non-interacting electrons. By employing boundary conformal field theory techniques we show that the differential capacitance of the box exhibits manifest two-channel Kondo scaling with temperature and gate voltage, uncontaminated by the one-dimensional electron correlations. We discuss the prospect to experimentally access the Kondo regime with this type of device.
We suggest an experiment to study Luttinger liquid behavior in a one-dimensional nanostructure, avoiding the usual complications associated with transport measurements. The proposed setup consists of a quantum box, biased by a gate voltage, and side coupled to a quantum wire by a point contact. Close to the degeneracy points of the Coulomb blockaded box, and in the presence of a magnetic field sufficiently strong to spin polarize the electrons, the setup can be described as a Luttinger liquid interacting with an effective Kondo impurity. Using exact nonperturbative techniques, we predict that the differential capacitance of the box will exhibit distinctive Luttinger liquid scaling with temperature and gate voltage.
The noncrossing approximation (NCA) is generalized to the multichannel Kondo-spin Hamiltonian with arbitrary anisotropic exchange couplings and an external magnetic field, and applied---in the framework of Matveev's mapping---to the charge fluctuations in a single-electron box at the Coulomb blockade. The temperature dependences of the charge step and the capacitance are calculated for a narrow point contact. At low temperatures and close to the degeneracy point, the capacitance line shape exhibits an approximate scaling with U/T,U/\sqrt{T},U/T​, where U is the deviation in gate voltage from the degeneracy point. This scaling relation is proposed as a sharp experimental diagnostic for the non-Fermi-liquid physics of the system at low temperatures. Both the reliability and shortcomings of the Kondo NCA are discussed in detail. Through comparison with poor-man's scaling, we are able to pinpoint the omission of particle-particle processes as the origin of the NCA flaws. An extended diagrammatic scheme is devised to amend the NCA flaws.
In this Ph.D. thesis I present the background and providefurther details to the work presented in the appended papers. The background consists of brief overviews of Kondo physics, Luttinger liquid theory, and conformal field theory. My own research is divided into three parts: the first deals with the interplay between Luttinger and Kondo physics (described in Papers I and II), the secondaddresses scanning tunneling microscopy (STM) response of a Luttinger liquid with an edge or an impurity (described in Paper III), and the third explores the boundary Green's function of 1D electrons in the spin-incoherent regime (described in Paper IV). In Papers I and II a setup is proposed which allows for acontrolled study of Kondo and Luttinger liquid physics. Itconsists of a quantum box, biased by a gate voltage, and side-coupled to a quantum wire by a point contact. Close to the degeneracy points of the Coulomb blockaded box the setup can be described as a Luttinger liquid interacting with an effective Kondo impurity. Using boundary conformal field theory techniques we predict that for the case of spin-polarized electrons the differential capacitance of the box will exhibit distinctive Luttinger liquid scaling with temperature and gate voltage. In the limit of zero magnetic field the Luttinger liquid behavior gets masked by two-channel Kondo screening, leading to a logarithmic scaling of the differential capacitance with temperatureand gate voltage. These effects should be possible to studyexperimentally, using the recently developed single-electrontransistor (SET) electrometer technique.In Paper III the finite-temperature local spectral weight (LSW) of a Luttinger liquid with a hard wall boundary is calculated. Close to the boundary the LSW exhibits characteristic oscillations indicative of spin-charge separation. The line shape of the LSW is also found to have a Fano-like asymmetry, a feature originating from the combined effect of electron-electron interaction and scattering off the boundary. Our results can be used to predict how edges and impurities influencethe STM response of one-dimensional electron systemsat low temperatures and voltage bias. Applications to STM onsingle-walled carbon nanotubes are also discussed.Paper IV, finally, presents a study of the spin-incoherent regime of 1D strongly interacting electrons. For sufficiently low densities the potential energy dominates the kinetic energy, and one can easily reach thespin-incoherent regime where the spin exchange energy is much less than the temperature. We have generalized the description of the spin-incoherent regime to account for the presence of a boundary. By calculating the exact Green's function we find that the charge sector critical exponent is highly sensitive to the boundary, strongly modifying the tunneling of electrons close to it. Our approach also allows for a detailed description of the crossover between boundary and bulk regimes.
In this document we present a study of the thermodynamic and transport properties of two kinds of quantum impurity systems in the Kondo regime.The first system consists of a spin-1 molecule in which mechanical stretching along the transport axis produces a magnetic anisotropy.We find that a generic coupling between a vibrational mode along this axis and the molecular spin induces a correction to the magnetic anisotropy, driving the ground state of the system into a non-Fermi-liquid phase.A transition into a Fermi-liquid ground state can then be induced by means of stretching, going through an underscreened spin-1 Kondo ground state at zero effective anisotropy.In the second system we study the effects of a charge detector, implemented by a quantum point-contact (QPC), on the Kondo state of a nearby spin-1/2 quantum dot (QD).While making the charge detection possible, the Coulomb interaction between the electrons traversing the QPC and those within the QD contribute to decoherence of the Kondo state.By modeling the QPC as two metallic terminals connected to an intermediate localized level, we can explore three transport regimes of the detector: a zero-conductance regime, a finite-conductance regime in mixed valence, and unitary conductance in a Kondo ground state that has been suggested as an explanation to the "0.7 anomaly" in QPCs.Transitions between these different ground states can be achieved by tuning the strength of a capacitive coupling that parameterizes the electrostatic interaction.
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.