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Abstract
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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 system and for two types of Schrödinger 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 Schrödinger and Dirac
carriers. While the curved surface increases the RKKY interaction strength for Schrödinger-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 electron density on the exchange interaction mediated by these carriers.
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