Non-perturbative effects and indirect exchange interaction between quantum impurities on metallic (111) surfaces

TL;DR

This paper models the complex interplay of surface and bulk states on noble metal (111) surfaces, revealing non-perturbative effects on quantum impurities and how bulk states influence RKKY interactions and screening.

Contribution

It introduces an effective tight-binding model including bulk states and uses DMRG to study quantum impurity interactions non-perturbatively on metallic surfaces.

Findings

Bulk states alter RKKY interaction periods.

Screening and exchange are enhanced by bulk contributions.

Ferromagnetism is suppressed except at very short distances.

Abstract

The (111) surface of noble metals is usually treated as an isolated two dimensional (2D) triangular lattice completely decoupled from the bulk. However, unlike topological insulators, other bulk bands cross the Fermi level. We here introduce an effective tight-binding model that accurately reproduces results from first principles calculations, accounting for both surface and bulk states. We numerically solve the many-body problem of two quantum impurities sitting on the surface by means of the density matrix renormalization group. By performing simulations in a star geometry, we are able to study the non-perturbative problem in the thermodynamic limit with machine precision accuracy. We find that there is a non-trivial competition between Kondo and RKKY physics and as a consequence, ferromagnetism is never developed, except at short distances. The bulk introduces a variation in the period of the RKKY interactions, and therefore the problem departs considerably from the simpler 2D case. In addition, screening, and the magnitude of the effective indirect exchange is enhanced by the contributions from the bulk states.