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Register a new userLarge-N Approach to the Two-Channel Kondo Lattice
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This paper studies the two-channel Kondo lattice in the large-N limit at half-filling. In this model, the continuous channel-symmetry is spontaneously broken, forming a channel ferromagnet in which one conduction channel forms a Kondo insulator, while the other remains conducting. The paper discusses how this ground-state can be understood using the concept of order fractionalization, in which the channel magnetization breaks up into an emergent spinor order parameter. By integrating out the fermions we derive an effective action that describes this symmetry breaking and its emergent collective modes. A remarkable observation is that topological defects in the order parameter carry a U(1) flux, manifested in the Aharonov-Bohm phase picked by electrons that orbit the defect. By studying the effective action, we argue that the phase diagram contains a non-magnetic transition between a large and a small Fermi surface.
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We have studied the energy spectrum of a one-dimensional Kondo lattice, where the localized magnetic moments have SU(N) symmetry and two channels of conduction electrons are present. At half filling, the system is shown to exist in two phases: one dominated by RKKY-exchange interaction effects, and the other by Kondo screening. A quantum phase transition point separates these two regimes at temperature $T = 0$. The Kondo-dominated phase is shown to possess soft modes, with spectral gaps much smaller than the Kondo temperature.
In the first step, experiments on a single cerium or ytterbium Kondo impurity reveal the importance of the Kondo temperature by comparison to other type of couplings like the hyperfine interaction, the crystal field and the intersite coupling. The extension to a lattice is discussed. Emphasis is given on the fact that the occupation number $n_f$ of the trivalent configuration may be the implicit key variable even for the Kondo lattice. Three $(P, H, T)$ phase diagrams are discussed: CeRu$_2$Si$_2$, CeRhIn$_5$ and SmS.
We address the origin of the magnetic-field independent -|A| T^{1/2} term observed in the low-temperature resistivity of several As-based metallic systems of the PbFCl structure type. For the layered compound ZrAs_{1.58}Se_{0.39}, we show that vacancies in the square nets of As give rise to the low-temperature transport anomaly over a wide temperature regime of almost two decades in temperature. This low-temperature behavior is in line with the non-magnetic version of the two-channel Kondo effect, whose origin we ascribe to a dynamic Jahn-Teller effect operating at the vacancy-carrying As layer with a C_4 symmetry. The pair-breaking nature of the dynamical defects in the square nets of As explains the low superconducting transition temperature T_{rm{c}}approx 0.14 K of ZrAs_{1.58}Se_{0.39}, as compared to the free-of-vacancies homologue ZrP_{1.54}S_{0.46} (T_{rm{c}}approx 3.7 K). Our findings should be relevant to a wide class of metals with disordered pnictogen layers.
For a mobile spin-1/2 impurity, coupled antiferromagnetically to a one-dimensional gas of fermions, perturbative ideas have been used to argue in favor of two-channel Kondo behavior of the impurity spin. Here we combine general considerations and extensive numerical simulations to show that the problem displays a novel quantum phase transition between two-channel and one-channel Kondo screening upon increasing the Kondo coupling. We construct a ground-state phase diagram and discuss the various non-trivial crossovers as well as possible experimental realizations.
We consider the Kondo effect in Y-junctions of anisotropic XY models in an applied magnetic field along the critical lines characterized by a gapless excitation spectrum. We find that, while the boundary interaction Hamiltonian describing the junction can be recasted in the form of a four-channel, spin-1/2 antiferromagnetic Kondo Hamiltonian, the number of channels effectively participating in the Kondo effect depends on the chain parameters, as well as on the boundary couplings at the junction. The system evolves from an effective four-channel topological Kondo effect for a junction of XX-chains with symmetric boundary couplings into a two-channel one at a junction of three quantum critical Ising chains. The effective number of Kondo channels depends on the properties of the boundary and of the bulk. The XX-line is a critical line, where a four-channel topological Kondo effect can be recovered by fine-tuning the boundary parameter, while along the line in parameter space connecting the extreme regimes, XX-line and the critical Ising point the junction is effectively equivalent to a two-channel topological Kondo Hamiltonian. Using a renormalization group approach, we determine the flow of the boundary couplings, which allows us to define and estimate the critical couplings and Kondo temperatures of the different Kondo (pair) channels. Finally, we study the local transverse magnetization in the center of the Y-junction, eventually arguing that it provides an effective tool to monitor the onset of the two-channel Kondo effect.
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