73 research outputs found
Kondo Temperature for the Two-Channel Kondo Models of Tunneling Centers
The possibility for a two-channel Kondo () 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, . We prove that, in
contrast to previous believes, the contribution of higher excited states in DWP
does not enhance . On the contrary, is reduced by three orders of
magnitude as compared with the two-level model: the prefactor in is
determined by the spacing between the second and the third levels in DWP rather
than by the electron Fermi energy. Moreover, , 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 phenomenology.Comment: 5 pages, 4 .eps figure
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
Effect of Anharmonicity on the Kondo Phenomena of a Magnetic Ion Vibrating in a Confinement Potential
Effect of anharmonicity of a cage potential for a magnetic ion vibrating in a
metal is investigated by the numerical renormalization group method. The cage
potential is assumed to be one-dimensional and of the double-well type. In the
absence of the Coulomb interaction, we find continuous crossover among the
three limiting cases: Yu-Anderson-type Kondo regime, the double-well-type Kondo
one, and the renormalized Fermi chain one. In the entire parameter space of the
double-well potential, the ground state is described by a local Fermi liquid.
In the Yu-Anderson-type Kondo regime, a quantum phase transition to the ground
state with odd parity takes place passing through the two-channel Kondo fixed
point when the Coulomb interaction increases. Therefore, the vibration of a
magnetic ion in an oversized cage structure is a promising route to the
two-channel Kondo effect.Comment: 6 pages, 3 figures, accepted for JPS
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 SmOsSb, some
other filled-skutterudites, and clathrate compounds.Comment: 9 pages, 7 figures. Added references and "Note added
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
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.
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 , 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.
Theory of inelastic scattering from quantum impurities
We use the framework set up recently to compute non-perturbatively inelastic
scattering from quantum impurities [G. Zar\'and {\it et al.}, Phys. Rev. Lett.
{\bf 93}, 107204 (2004)] to study the the energy dependence of the single
particle -matrix and the inelastic scattering cross section for a number of
quantum impurity models. We study the case of the spin two-channel
Kondo model, the Anderson model, and the usual single-channel Kondo
model. We discuss the difference between non-Fermi liquid and Fermi liquid
models and study how a cross-over between the non-Fermi liquid and Fermi liquid
regimes appears in case of channel anisotropy for the two-channel Kondo
model. We show that for the most elementary non-Fermi liquid system, the
two-channel Kondo model, half of the scattering remains inelastic even at the
Fermi energy. Details of the derivation of the reduction formulas and a simple
path integral approach to connect the -matrix to local correlation functions
are also presented.Comment: published versio
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 is computed as a function of
barrier parameters. We find that for special parameters can be close to
and it can be of the same order of magnitude as the renormalized
splitting . 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 remains
unrenormalized at energies above the Debye frequency, .Comment: 9 pages, 9 figures, RevTe
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