RKKY couplings in the Lieb lattice: flat-band induced frustration

Abstract: Despite their dispersion-less character, flat bands (FBs) are often at the heart of remarkable physical phenomena. Because, FBs may be responsible for unconventional quantum electronic transport, our purpose is to investigate their impact on the RKKY couplings (J(R)). As a good candidate, we choose the The Lieb lattice which consists of one four-fold coordinated atom (A) and two two-fold coordinated atoms (B,C) per unit cell. As in graphene, at the neutrality point, J(R) is found to fall off as 1/R3. The coupling between a pair of impurities on sublattice A are found ferromagnetic and isotropic. In contrast, for impurities on the two-fold coordinated sites, J(R) reveals (i) a strong angular anisotropy and (ii) can be both ferromagnetic (F) or antiferromagnetic (AF). The AF character introduced by the FB can largely dominate, and introduces frustration effects. The FB is found to have a drastic impact on J(R) for impurities located on (B,C) sublattices. We have also addressed the effect of tuning the carrier density that reveals remarkable features as well.