Article

# Dynamical correlations in the spin-half two-channel Kondo model

Physical review. B, Condensed matter (Impact Factor: 3.77). 01/2008; DOI: 10.1103/PhysRevB.78.165130

Source: arXiv

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**ABSTRACT:**An exact expression is derived for the electron Green function in two-channel Kondo models with one and two impurities, describing the crossover from non-Fermi liquid (NFL) behavior at intermediate temperatures to standard Fermi liquid (FL) physics at low temperatures. Symmetry-breaking perturbations generically present in experiment ensure the standard low-energy FL description, but the full crossover is wholly characteristic of the unstable NFL state. Distinctive conductance lineshapes in quantum dot devices should result. We exploit a connection between this crossover and one occurring in a classical boundary Ising model to calculate real-space electron densities at finite temperature. The single universal finite-temperature Green function is then extracted by inverting the integral transformation relating these Friedel oscillations to the t matrix. Excellent agreement is demonstrated between exact results and full numerical renormalization group calculations.Physical review. B, Condensed matter 03/2012; 85(23). · 3.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We study odd-membered chains of spin-(1/2) impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong inter-impurity coupling, a residual chain spin-(1/2) moment experiences a renormalized effective coupling to the leads; while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models where the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even-fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is non-zero and determined solely by the `excess' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where inter-lead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of these problems.Physical review. B, Condensed matter 03/2011; 84. · 3.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**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.Physical review. B, Condensed matter 06/2008; 77(24). · 3.77 Impact Factor

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