RKKY interaction on curved surfaces: Different behavior of Dirac and Schr\"{o}dinger carriers as interaction mediating particles

TL;DR

This study examines how the curvature of a surface influences the RKKY interaction between impurities, revealing contrasting effects on Schr"odinger and Dirac carriers, with implications for two-dimensional materials like graphene.

Contribution

It provides a comparative analysis of RKKY interactions on curved surfaces for Schr"odinger and Dirac particles, highlighting the geometry-dependent behavior of these carriers.

Findings

Curvature enhances RKKY interaction for Schr"odinger carriers.

Curvature reduces RKKY interaction for Dirac carriers.

LDOS correlates with RKKY interaction strength.

Abstract

The RKKY interaction between two impurities on a curved surface is investigated. Practical curved sample parameters are considered for investigating curvatures, similar to those observed experimentally in available samples such as graphene. For this type of two-dimensional curved systems and for two types of Schr\"{o}dinger and Dirac carriers, the RKKY interaction and local density of states (LDOS) are calculated. Results show that the strength of the RKKY interaction on a curved surface depends significantly on the nature of particles embedded on this surface, indicating that the geometry has a different effect on the dynamics of Schr\"{o}dinger and Dirac carriers. While the curved surface increases the RKKY interaction strength for Schr\"{o}dinger-type carriers in comparison with the flat sample, RKKY interaction decreases in the curved surface for Dirac-type particles. This can be understood regrading the effective magnetic field experienced by the Dirac particles as a result of the curved surface. There is also a correlation between LDOS and the RKKY interaction, which could be explained by the effect of conducting electrons density on the exchange interaction mediated by these carriers.