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We consider odd-membered chains of antiferromagnetically (AF) coupled spin-1/2 impurities,
with each end connected to its own metallic lead. Two-channel Kondo (2CK) physics is shown to arise
generically at low energies, with two overscreening mechanisms found to occur depending on coupling
strength, each giving rise to distinct signatures in physical properties. We also discuss 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. 2CK
physics is shown to be wholly robust to variable dot filling provided mirror symmetry is preserved. In
particular, the single-particle spectrum at the Fermi level - and hence the low-temperature zero-bias
conductance - is always pinned to half-unitarity; with interesting consequences, via a generalised Friedel-Luttinger sum rule, for the Luttinger integral of this non-Fermi liquid phase.
We also consider a ring of three AF-coupled quantum dots, tunnel-coupled to two metallic leads - probably the simplest model in which the consequences of local frustration arising from internal degrees of freedom may be studied in a 2-channel environment. While 2CK physics again predominates at low-energies in the mirror-symmetric models considered, two distinct 2CK phases, with different ground state parities, necessarily arise on tuning the interdot exchange couplings. In consequence, a frustration-induced quantum phase transition occurs, the 2CK phases being separated by a quantum critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasi-degenerate local trimer states destabilises the 2CK fixed points; and the critical fixed point is shown to consist of a free pseudospin together with effective 1-channel spin quenching, itself reflecting underlying channel-anisotropy in the inherently 2-channel system. Numerical renormalization group and related methods are used to obtain a detailed understanding of these problems, including study of both thermodynamic and dynamical properties of the systems. |
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