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arXiv:1111.6503 · Physical Review Letters

Two-Channel Kondo Physics in Two-Impurity Kondo Models

Andrew K. Mitchell, Eran Sela, David E. Logan

Published Feb 24, 2012• 64 citations
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Abstract

We consider the non-Fermi-liquid quantum critical state of the spin-S two-impurity Kondo model and its potential realization in a quantum dot device. Using conformal field theory and the numerical renormalization group, we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin S. Distinct conductance signatures are shown to arise as a function of device asymmetry, with the square-root behavior commonly believed to arise at low-energies dominant only in certain regimes.

DOI
10.1103/physrevlett.108.086405

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We consider the non-Fermi-liquid quantum critical state of the spin-S two-impurity Kondo model and its potential realization in a quantum dot device. Using conformal field theory and the numerical renormalization group, we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin S. Distinct conductance signatures are shown to arise as a function of device asymmetry, with the square-root behavior commonly believed to arise at low-energies dominant only in certain regimes.
We study finite-frequency transport properties of the double dot system recently constructed to observe the two-channel Kondo effect [R. M. Potok et al., Nature 446, 167 (2007)]. We derive an analytical expression for the frequency-dependent linear conductance of this device in the Kondo regime. We show how the features characteristic of the two-channel Kondo quantum critical point emerge in this quantity, which we compute using the results of conformal field theory as well as numerical renormalization group methods. We determine the universal crossover functions describing non-Fermi-liquid vs Fermi-liquid crossovers and also investigate the effects of a finite magnetic field.
The long-thought charge Kondo effects have recently been experimentally realized in the quantum Hall regime. This experiment, supported by numerics, exemplifies the realization of two-channel Kondo state, a non-Fermi Liquid, and its crossover to the one-channel counterpart, a Fermi liquid. Scaling up such a platform, we find a hierarchy of non-Fermi Liquids and their tunable crossovers based on a renormalization group analysis. Utilizing results from a conformal field theory, we further examine the universal conductances of this strongly correlated system and their finite temperature scaling, which elucidate the sharp distinctions between charge and spin Kondo physics.
The two-impurity Kondo Hamiltonian is known to possess a multicritical point separating stable Fermi-liquid phases in which the two impurities either form a singlet or else are screened by the conduction electrons. We propose an exact critical theory for this non-Fermi-liquid multicritical point, using conformal field theory methods, which predicts all critical properties including the finite-size spectrum, specific heat, susceptibilities, renormalization-group behavior, residual entropy, scattering matrix, and local pair Green's function.
The two-impurity Kondo model with particle-hole symmetry is known to have a critical point at comparable RKKY interaction and Kondo temperature. Using bosonization and controlled low energy projection, we identify the critical point and map it to a solvable resonant level model. The physics of the critical point is shown to be the same as the two-channel Kondo model. An effective Hamiltonian is derived from which the solutions for the critical point and surrounding Fermi-liquid phase follow immediately. The universality of the critical point is strongly supported by the overall excellent agreement with the numerical renormalization group and conformal field theory results.
Numerical renormalization-group and conformal-field-theory work indicate that the two-impurity Kondo Hamiltonian has a non-Fermi-liquid critical point separating the Kondo-screening phase from the interimpurity singlet phase when particle-hole (P-H) symmetry is maintained. We clarify the circumstances under which this critical point occurs, pointing out that there are two types of P-H symmetry. Only one of them guarantees the occurrence of the critical point. Much of the previous numerical work was done on models with the other type of P-H symmetry. We analyze this critical point using the boundary conformal-field-theory technique. The finite-size spectrum is presented in detail and compared with about 50 energy levels obtained using the numerical renormalization group. Various Green's functions, general renormalization group behavior, and a hidden SO(7) are analyzed.
Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.