RKKY interaction on the surface of three-dimensional Dirac semimetals

Abstract

We study the RKKY interaction between two magnetic impurities located on the surface of a three-dimensional Dirac semimetal with two Dirac nodes in the band structure. By taking into account both bulk and surface contributions to the exchange interaction between the localized spins, we demonstrate that the surface contribution in general dominates the bulk one at distances larger than the inverse node separation due to a weaker power-law decay. We find a strong anisotropy of the surface term with respect to the spins being aligned along the node separation axis or perpendicular to it. In the many impurity dilute regime, this implies formation of quasi-one-dimensional magnetic stripes orthogonal to the node axis. We also discuss the effects of a surface spin-mixing term coupling electrons from spin-degenerate Fermi arcs. arXiv:1811.05750v3 [cond-mat.mes-hall]

RKKY Interaction in Graphene at Finite Temperature

“…Actually, while rederiving Equations (28) and (29) we have found additional multiplier 1/2π, but since we were already quite sloppy with the numerical multiplier in going from summation to integration in Equation 14, we decided to leave the equations in this paper as they were in the previously published one [47]. In any case, Equations (24) and (26) are valid independently of the presence of additional multiplier for χ T=0 .…”

“…RKKY interaction has been investigated in materials of different nature such as disordered metals [4], superconductors [5][6][7], topological insulators [8][9][10][11][12][13][14][15], carbon nanotubes [16,17], semiconducting wires [18], in Weyl and Dirac semimetals [19][20][21][22][23][24], but most thoroughly in graphene . RKKY interaction in graphene is also the subject of the present publication.…”

RKKY coupling in Weyl semimetal thin films

“…For a semi-infinite system, it can be shown for large r that the elements of the Green's function G( r) asymptotically vanish as ∼ 1/r 2 when r is on the surface and r ŷ. By contrast, they fall off as ∼ 1/r when r points along thex direction 19 ; the difference is a consequence of the (nearly) unidirectional dispersion of the Fermi arc energies. This results in the strongest RKKY coupling for impurities separated along thex direction, and in what follows we focus on separations along this direction.…”

“…This difference from Eqs. 36 is expected due to the curvature of the Fermi arcs 19 . Off-diagonal components other than J zy and J yz (not shown) are several orders of magnitude smaller than these quantities, as expected from the above analysis.…”

“…Moreover, for a thick enough sample (when the presence of the other surface may be neglected), states in each of the Fermi arcs are spin-polarized (along the direction of σ x in our model) and are chiral in their dispersion (i.e, the energy is proportional to ±k x for η = ±1). One expects in this case that the RKKY interaction J xx will be vanishingly small 10,18,19 .…”