Kondo Temperature for the Two-Channel Kondo Models of Tunneling Centers

The possibility for a two-channel Kondo ($2CK$) non Fermi liquid state to appear in a metal as a result of the interaction between electrons and movable structural defects is revisited. As usual, the defect is modeled by a heavy particle moving in an almost symmetric double-well potential (DWP). Taking into account only the two lowest states in DWP is known to lead to a Kondo-like Hamiltonian with rather low Kondo temperature, $T_K$. We prove that, in contrast to previous believes, the contribution of higher excited states in DWP does not enhance $T_K$. On the contrary, $T_K$ is reduced by three orders of magnitude as compared with the two-level model: the prefactor in $T_K$ is determined by the spacing between the second and the third levels in DWP rather than by the electron Fermi energy. Moreover, $T_K$, turns out to be parametrically smaller than the splitting between the two lowest levels. Therefore, there is no microscopic model of movable defects which may justify non-Fermi liquid $2CK$ phenomenology.Comment: 5 pages, 4 .eps figure

Local Heavy Quasiparticle in Four-Level Kondo Model

An impurity four-level Kondo model, in which an ion is tunneling among 4-stable points and interacting with surrounding conduction electrons, is investigated using both perturbative and numerical renormalization group methods. The results of numerical renormalization group studies show that it is possible to construct the ground state wavefunction including the excited ion states if we take into account the interaction between the conduction electrons and the ion. The resultant effective mass of quasiparticles is moderately enhanced. This result offers a good explanation for the enhanced and magnetically robust Sommerfeld coefficient observed in SmOs$_4$Sb$_{12}$, some other filled-skutterudites, and clathrate compounds.Comment: 9 pages, 7 figures. Added references and "Note added

Dynamics of Tunneling Centers in Metallic Systems

Dynamics of tunneling centers (TC) in metallic systems is studied, using the technique of bosonization. The interaction of the TC with the conduction electrons of the metal involves two processes, namely, the screening of the TC by electrons, and the so-called electron assisted tunneling. The presence of the latter process leads to a different form of the renormalized tunneling frequency of the TC, and the tunneling motion is damped with a temperature dependent relaxation rate. As the temperature is lowered, the relaxation rate per temperature shows a steep rise as opposed to that in the absence of electron assisted process. It is expected that this behavior should be observed at very low temperatures in a careful experiment. The present work thus tries to go beyond the existing work on the {\it dynamics} of a two-level system in metals, by treating the electron assisted process.Comment: REVTeX twocolumn format, 5 pages, two PostScript figures available on request. Preprint # : imsc 94/3

Instability of the marginal commutative model of tunneling centers interacting with metallic environment: Role of the electron-hole symmetry breaking

The role of the electron-hole symmetry breaking is investigated for a symmetrical commutative two-level system in a metal using the multiplicative renormalization group in a straightforward way. The role of the symmetries of the model and the path integral technique are also discussed in detail. It is shown that the electron-hole symmetry breaking may make the model non-commutative and generate the assisted tunneling process which is, however, too small itself to drive the system into the vicinity of the two-channel Kondo fixed point. While these results are in qualitative agreement with those of Moustakas and Fisher (Phys. Rev. B 51, 6908 (1995), ibid 53, 4300 (1996)) the scaling equations turn out to be essentially different. We show that the main reason for this difference is that the procedure for the elimination of the high energy degrees of freedom used by Moustakas and Fisher leaves only the free energy invariant, however, the couplings generated are not connected to the dynamical properties in a straightforward way and should be interpreted with care. These latter results might have important consequences in other cases where the path integral technique is used to produce the scaling equations and calculate physical quantities.Comment: latex, figures in ps file adde

Kondo Effect in Systems with Spin Disorder

We consider the role of static disorder in the spin sector of the one- and two-channel Kondo models. The distribution functions of the disorder-induced effective energy splitting between the two levels of the Kondo impurity are derived to the lowest order in the concentration of static scatterers. It is demonstrated that the distribution functions are strongly asymmetric, with the typical splitting being parametrically smaller than the average rms value. We employ the derived distribution function of splittings to study the temperature dependence of the low-temperature conductance of a sample containing an ensemble of two-channel Kondo impurities. The results are used to analyze the consistency of the two-channel Kondo interpretation of the zero-bias anomalies observed in Cu/(Si:N)/Cu nanoconstrictions.Comment: 16 pages, 5 figures, REVTe

Dephasing in Metals by Two-Level Systems in the 2-Channel-Kondo Regime

We point out a novel, non-universal contribution to the dephasing rate 1/\tau_\phi \equiv \gamma_\phi of conduction electrons in metallic systems: scattering off non-magnetic two-level systems (TLSs) having almost degenerate Kondo ground states. In the regime \Delta_{ren} < T < T_K (\Delta_{ren} = renormalized level splitting, T_K = Kondo temperature), such TLSs exhibit non-Fermi-liquid physics that can cause \gamma_\phi, which generally decreases with decreasing T, to seemingly saturate in a limited temperature range before vanishing for T \to 0. This could explain the saturation of dephasing recently observed in gold wires [Mohanty et al. Phys. Rev. Lett. 78, 3366 (1997)].Comment: Final published version, including minor improvements suggested by referees. 4 pages, Revtex, 1 figur

Simple Bosonization Solution of the 2-channel Kondo Model: I. Analytical Calculation of Finite-Size Crossover Spectrum

We present in detail a simple, exact solution of the anisotropic 2-channel Kondo (2CK) model at its Toulouse point. We reduce the model to a quadratic resonant-level model by generalizing the bosonization-refermionization approach of Emery and Kivelson to finite system size, but improve their method in two ways: firstly, we construct all boson fields and Klein factors explicitly in terms of the model's original fermion operators $c_{k \sigma j}$, and secondly we clarify explicitly how the Klein factors needed when refermionizing act on the original Fock space. This enables us to explicitly follow the adiabatic evolution of the 2CK model's free-fermion states to its exact eigenstates, found by simply diagonalizing the resonant-level model for arbitrary magnetic fields and spin-flip coupling strengths. In this way we obtain an {\em analytic} description of the cross-over from the free to the non-Fermi-liquid fixed point. At the latter, it is remarkably simple to recover the conformal field theory results for the finite-size spectrum (implying a direct proof of Affleck and Ludwig's fusion hypothesis). By analyzing the finite-size spectrum, we directly obtain the operator content of the 2CK fixed point and the dimension of various relevant and irrelevant perturbations. Our method can easily be generalized to include various symmetry-breaking perturbations. Furthermore it establishes instructive connections between different renormalization group schemes such as poor man's scaling, Anderson-Yuval type scaling, the numerical renormalization group and finite-size scaling.Comment: 35 pages Revtex, 7 figures, submitted to Phys. Rev.

Orbital Kondo behavior from dynamical structural defects

The interaction between an atom moving in a model double-well potential and the conduction electrons is treated using renormalization group methods in next-to-leading logarithmic order. A large number of excited states is taken into account and the Kondo temperature $T_K$ is computed as a function of barrier parameters. We find that for special parameters $T_K$ can be close to $1 {\rm K}$ and it can be of the same order of magnitude as the renormalized splitting $\Delta$. However, in the perturbative regime we always find that T_K \alt \Delta with a T_K \alt 1 {\rm K} [Aleiner {\em et al.}, Phys. Rev. Lett. {\bf 86}, 2629 (2001)]. We also find that $\Delta$ remains unrenormalized at energies above the Debye frequency, $\omega_{\rm Debye}$.Comment: 9 pages, 9 figures, RevTe

Two-Channel Kondo Physics from Tunnelling Impurities with Triangular Symmetry

Tunnelling impurities in metals have been known for some time to have the potential for exhibiting Kondo-like physics. However previous models based on an impurity hopping between two equivalent positions have run into trouble due to the existence of relevant operators that drive the system away from the non-Fermi-liquid Kondo fixed point. In the case of an impurity hopping among positions with higher symmetry, such as triangular symmetry, it is shown here that the non-Fermi-liquid behavior at low temperatures can be generic. Using various bosonization techniques, the fixed point is shown to be {\em stable}. However, unlike the conventional two-channel Kondo (2CK) model, it has {\em four} leading irrelevant operators, implying that while the form of the singular temperature dependence of physical quantities is similar to the 2CK model, there will not be simple universal amplitude ratios. The phase diagram of this system is analyzed and a critical manifold is found to separate the non-Fermi-liquid from a conventional Fermi liquid fixed point. Generalization to higher symmetries, such as cubic, and the possibility of physical realizations with dynamic Jahn-Teller impurities is discussed.Comment: 20 pages, 4 figures, RevTex format, submitted to Phys. Rev.

Finite-Size Bosonization of 2-Channel Kondo Model: a Bridge between Numerical Renormalization Group and Conformal Field Theory

We generalize Emery and Kivelson's (EK) bosonization-refermionization treatment of the 2-channel Kondo model to finite system size and on the EK-line analytically construct its exact eigenstates and finite-size spectrum. The latter crosses over to conformal field theory's (CFT) universal non-Fermi-liquid spectrum (and yields the most-relevant operators' dimensions), and further to a Fermi-liquid spectrum in a finite magnetic field. Our approach elucidates the relation between bosonization, scaling techniques, the numerical renormalization group (NRG) and CFT. All CFT's Green's functions are recovered with remarkable ease from the model's scattering states.Comment: 4 pages, 1 figure, Revte