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Abstract:

We consider an interacting nanowire/superconductor heterostructure attached to metallic leads. The device is described by an unusual low-energy model involving spin-1 conduction electrons coupled to a nonlocal spin-1/2 Kondo impurity built from Majorana fermions. The topological origin of the resulting Kondo effect is manifest in distinctive non-Fermi-liquid (NFL) behavior, and the existence of Majorana fermions in the device is demonstrated unambiguously by distinctive conductance lineshapes. We study the physics of the model in detail, using the numerical renormalization group, perturbative scaling and abelian bosonization. In particular, we calculate the full scaling curves for the differential conductance in AC and DC fields, onto which experimental data should collapse. Scattering t-matrices and thermodynamic quantities are also calculated, recovering asymptotes from conformal field theory. We show that the NFL physics is robust to asymmetric Majorana-lead couplings, and here we uncover a duality between strong and weak coupling. The NFL behavior is understood physically in terms of competing Kondo effects. The resulting frustration is relieved by inter-Majorana coupling which generates a second crossover to a regular Fermi liquid.

Abstract:

The Numerical Renormalization Group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within DMFT. Here we present a simple generalization of the Wilson Chain, which improves the scaling of computational cost with the number of channels/bands, bringing new problems within reach. The method is applied to calculate the t-matrix of the three-channel Kondo model at T=0, which shows universal crossovers near non-Fermi liquid critical points. A non-integrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening/overscreening mechanisms.

Abstract:

We study theoretically a triangular cluster of three magnetic impurities, hybridizing locally with conduction electrons of a metallic host. Such a cluster is the simplest to exhibit frustration - an important generic feature of many complex molecular systems in which different interactions compete. Here, low-energy doublet states of the trimer are favored by effective exchange interactions produced by strong electronic repulsion in localized impurity orbitals. Parity symmetry protects a level-crossing of such states on tuning microscopic parameters, while an avoided crossing arises in the general distorted case. On coupling to a metallic host, the behavior is shown to be immensely rich, since collective quantum many-body effects now also compete. In particular, impurity degrees of freedom are totally screened at low temperatures in a Kondo-screened Fermi liquid phase, while degenerate ground states persist in a local moment phase. Local frustration drives the quantum phase transition between the two, which may be first order or of Kosterlitz-Thouless type, depending on symmetries. Unusual mechanisms for local moment formation and Kondo screening are found, due to the orbital structure of the impurity trimer. Our results are of relevance for triple quantum dot devices. The problem is studied by a combination of analytical arguments and the numerical renormalization group.