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arXiv:cond-mat/0003013

Is the Multichannel Kondo Model Appropriate to Describe the Single Electron Transistor?

Gergely Zaránd, Gergely T. Zimányi, Frank K. Wilhelm

Published Mar 1, 2000• 0 citations
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Abstract

We investigate the low-temperature dynamics of single electron boxes and transistors close to their degeneracy point using renormalization group methods. We show that intermode scattering is a relevant perturbation and always drives the system to the two-channel Kondo fixed point, where the two channels correspond to the real spins of the conduction electrons. However, the crossover temperature T^*, below which Matveev's two-channel Kondo scenario [K.A. Matveev, Phys. Rev. B 51, 1743 (1995)] develops decreases exponentially with the number of conduction modes in the tunneling junctions and is extremely small in most cases. Above T^* the 'infinite channel model' of Ref.{onlinecite{Schoen}} turns out to be a rather good approximation. We discuss the experimental limitations and suggest a new experimental setup to observe the multichannel Kondo behavior.

DOI
10.48550/arxiv.cond-mat/0003013

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We investigate the low-temperature dynamics of single electron boxes and transistors close to their degeneracy point using renormalization group methods. We show that intermode scattering is a relevant perturbation and always drives the system to the two-channel Kondo fixed point, where the two channels correspond to the real spins of the conduction electrons. However, the crossover temperature T^, below which Matveev's two-channel Kondo scenario [K.A. Matveev, Phys. Rev. B 51, 1743 (1995)] develops decreases exponentially with the number of conduction modes in the tunneling junctions and is extremely small in most cases. Above T^ the 'infinite channel model' of Ref.{onlinecite{Schoen}} turns out to be a rather good approximation. We discuss the experimental limitations and suggest a new experimental setup to observe the multichannel Kondo behavior.
We investigate the low-temperature dynamics of single electron boxes and transistors close to their degeneracy point using renormalization-group methods. We show that intermode scattering is a relevant perturbation and always drives the system to the two-channel Kondo fixed point, where the two channels correspond to the real spins of the conduction electrons. However, the crossover temperature T∗,{T}^{*},T∗, below which Matveev's two-channel Kondo scenario [K.A. Matveev, Phys. Rev. B 51, 1743 (1995)] develops decreases exponentially with the number of conduction modes in the tunneling junctions and is extremely small in most cases. Above T∗{T}^{*}T∗ the ``infinite channel model'' of G. Falci, G. Sch\"on, and G.T. Zimany, Phys. Rev. Lett. 74, 3257 (1995) turns out to be a rather good approximation. We discuss the experimental limitations and suggest an experimental setup to observe the multichannel Kondo behavior.
A detailed and comprehensive study of the one-impurity multichannel Kondo model is presented. In the limit of a large number of conduction electron channels k>>1, the low-energy fixed point is accessible to a renormalization group improved perturbative expansion in 1/k. This straightforward approach enables us to examine the scaling, thermodynamics and dynamical response functions in great detail and make clear the following features: (i) the criticality of the fixed point, (ii) the universal non-integer degeneracy, and (iii) that the compensating spin cloud has a spatial extent of the order of one lattice spacing.
We consider an atom in a double-well potential [parametrized by a two-level system (TLS)] interacting with screened conduction electrons. The tunneling of the TLS is assisted by the Fermi gas. Close to the strong-coupling fixed point the renormalization-group equations for the noncommutative model in the case of spinless fermions, but an arbitrary number of relevant orbital channels, lead to the n-channel Kondo problem with S=1/2. By solving the thermodynamic Bethe-ansatz equations for the n-channel Kondo problem numerically in the presence of a magnetic field, we discuss the low-temperature properties of the TLS close to the fixed point. The Zeeman splitting corresponds to the energy difference between the two positions of the tunneling atom. The atom is not localized at one of the potential minima. The susceptibility diverges as H\ensuremath{\rightarrow}0 and T\ensuremath{\rightarrow}0, indicating that the symmetric TLS is unstable against a local lattice deformation via coupling to phonons. The lattice distortion disappears above a critical temperature Tc{\mathit{T}}_{\mathit{c}}Tc​. The ground-state equilibrium situation of the TLS corresponds to H\ensuremath{\ne}0 and a Fermi-liquid picture applies. The values for the specific heat become very large as H\ensuremath{\rightarrow}0. For small fields the specific heat shows a double-peak structure, which is particularly pronounced for n=2.
In the multichannel Kondo effect, overscreening of a magnetic impurity by conduction electrons leads to a frustrated exotic ground state. It has been proposed that multichannel topological Kondo (MCTK) model involving topological Cooper pair boxes with M M Majorana modes [SO( M M ) “spin”] and N N spinless electron channels exhibits an exotic intermediate coupling fixed point. This intermediate fixed point has been analyzed through large- N N perturbative calculations, which gives a zero-temperature conductance decaying as 1/N^2 1 / N 2 in the large- N N limit. However, the conductance at this intermediate fixed point has not been calculated for generic N N . Using representation theory, we verify the existence of this intermediate-coupling fixed point and find the strong-coupling effective Hamiltonian for the case M=4 M = 4 . Using conformal field theory techniques for SO( M M ), we generalize the notion of overscreening and conclude that the MCTK model is an overscreened Kondo model. We find the fixed-point finite-size energy spectrum and the leading irrelevant operator (LIO). We express the fixed-point conductance in terms of the modular S-matrix of SO( M M ) for general N N , confirming the previous large- N N result. We describe the finite-temperature corrections to the conductance by the LIO and find that they are qualitatively different for the cases N=1 N = 1 and N≥2 N ≥ 2 due to the different fusion outcomes with the current operator. We also compare the multichannel topological Kondo model to the topological symplectic Kondo model.
We discuss a multichannel SU(N) Kondo model which displays nontrivial zero-temperature phase transitions due to a conduction electron density of states vanishing with a power law at the Fermi level. In a particular large- N limit, the system is described by coupled integral equations corresponding to a dynamic saddle point. We exactly determine the universal low-energy behavior of spectral densities at the scale-invariant fixed points, obtain anomalous exponents, and compute scaling functions describing the crossover near the quantum-critical points. We argue that our findings are relevant to recent experiments on impurity-doped d-wave superconductors.
We study triangular clusters of three spin-1/2 Kondo or Anderson impurities that are coupled to two conduction leads. In the case of Kondo impurities, the model takes the form of an antiferromagnetic Heisenberg ring with Kondo-type exchange coupling to continuum electrons. We show that this model exhibits many types of the behavior found in various simpler one- and two-impurity models, thereby enabling the study of crossovers between a number of Fermi-liquid (FL) and non-Fermi-liquid (NFL) fixed points. In particular, we explore a direct crossover between the two-impurity Kondo-model NFL fixed point and the two-channel Kondo-model NFL fixed point. We show that the concept of the two-stage Kondo effect applies even in the case when the first-stage Kondo state is of NFL type. In the case of Anderson impurities, we consider the transport properties of three coupled quantum dots. This class of models includes, as limiting cases, the familiar serial double quantum dot and triple quantum dot nanostructures. By extracting the quasiparticle scattering phase shifts, we compute the low-temperature conductance as a function of the interimpurity tunneling coupling. We point out that due to the existence of exponentially low-temperature scales, there is a parameter range where the stable ``zero-temperature'' fixed point is essentially never reached (not even in numerical renormalization group calculations). The zero-temperature conductance is then of no interest and it may only be meaningful to compute the conductance at finite temperature. This illustrates the perils of studying the conductance in the ground state and considering thermal fluctuations only as a small correction.