Kondo Impurities Coupled to a Helical Luttinger Liquid: RKKY-Kondo Physics Revisited.

We show that the paradigmatic Ruderman-Kittel-Kasuya-Yosida (RKKY) description of two local magnetic moments coupled to propagating electrons breaks down in helical Luttinger liquids when the electron interaction is stronger than some critical value. In this novel regime, the Kondo effect overwhelms the RKKY interaction over all macroscopic interimpurity distances. This phenomenon is a direct consequence of the helicity (realized, for instance, at edges of a time-reversal invariant topological insulator) and does not take place in usual (nonhelical) Luttinger liquids.

Duality of weak and strong scatterer in a Luttinger liquid coupled to massless bosons.

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons).

Density of states for almost-diagonal random matrices.

We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost-diagonal Hermitian random matrices. The matrices have independent random entries H(i > or =j) with small off-diagonal elements: <|H(i not equal to j)|2> << <|H(ii)|2> approximately 1. Using the recently suggested method of a virial expansion in the number of interacting energy levels [J.