RKKY interaction in a doped pseudospin-1 fermion system at finite temperature

TL;DR

This paper investigates the RKKY interaction in a pseudospin-1 fermion system with flat and dispersive bands, revealing new interaction types and strong temperature dependence influenced by flat band effects.

Contribution

It provides analytical expressions for RKKY interactions in the $ ext{alpha-} ext{T}_3$ model, highlighting the impact of flat bands and extending understanding beyond graphene-like systems.

Findings

Three types of RKKY interactions identified, including a new flat-band induced type.

Strong temperature dependence of impurity interactions at small doping levels.

Analytical formulas derived for various limiting cases and conditions.

Abstract

We study the RKKY interaction of magnetic impurities in the $\alpha-\mathcal{T}_3$ model which hosts pseudospin-1 fermions with two dispersive and one flat bands. By using the effective low-energy Hamiltonian we calculate the RKKY coupling for impurities placed on the same or different sublattices. We find that there are three types of interaction, which depend on the model parameter defining the relative strength of hoppings between sublattices, two of them can be reduced to graphene case while the third one is new and is due to the presence of a flat zero-energy band. We derive general analytical expressions for the RKKY interaction in terms of Mellin-Barnes type integrals and analyze different limiting cases. The cases of finite chemical potential and temperature, as well as asymptotic at large distances are considered. We show that the interaction between impurities located at different rim sites displays a very strong temperature dependence at small doping being a direct consequence of the flat band. The subtleties of the theorem for signs of the RKKY interaction at zero doping, as applied to the $\mathcal{T}_3$ lattice, related to the existence of a dispersionless flat band are discussed.