ABSTRACT
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.
ABSTRACT
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). We find that the duality relation, ΔWSΔWL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.
ABSTRACT
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. Phys. A 36, 8265 (2003)], we calculate the leading correction to the Poissonian DOS in the cases of the Gaussian orthogonal and unitary ensembles. We apply the general formula to the critical power-law banded random matrices and the unitary Moshe-Neuberger-Shapiro model and compare the DOS's of these models.
