Ruderman-Kittel-Kasuya-Yosida interaction in biased bilayer graphene

Abstract

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two contact magnetic impurities placed on bilayer graphene (BLG). We compute the interaction mediated by the carriers of the pristine and biased BLG as well as the conduction electrons of the doped system. The results are obtained from the linear-response expression for the susceptibility written in terms of the integral over lattice Green's functions. For the unbiased system, we obtain some analytical expressions in terms of the Meijer G-functions, which consist of the product of two oscillatory terms, one coming from the interference between the two Dirac points and the second coming from the Fermi momentum. In particular, for the undoped BLG, the system exhibits the RKKY interaction commensurate with its bipartite nature as expected from the particle-hole symmetry of the system. Furthermore, we explore a beating pattern of oscillations of the RKKY interaction in a highly doped BLG system within the four-band continuum model. Besides, we discuss the discrepancy between the short-range RKKY interaction calculated from the two-band model and that obtained from the four-band continuum model. The final results for the applied gate voltage are obtained numerically and are fitted with the functional forms based on the results for the unbiased case. In this case, we show that the long-range behavior is scaled with a momentum that depends on Fermi energy and gate voltage, allowing the possibility of tuning of the RKKY interaction by gate voltage.

Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon

“…The RKKY interaction is small such that measuring it experimentally is usually hard. However, using a high value of density of states on the edge of materials such as zigzag graphene nanoribbons [13], or band tunability of materials such as bilayer graphene [16], increases the chance to measure this quantity. Zero gapped edge states in graphene only happen in perfect zigzag edges, however, there are both edge modes and band tunability in silicence.…”

“…The RKKY interaction has been extensively studied in carbon based materials [7][8][9][10][11][12][13][14][15][16][17] and it can be experimentally measured from single-atomic magnetometry of a pair of magnetic atoms [18,19] and also magnetotransport measurements [20] based on the angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) experiments. While this interaction has a simple Heisenberg term for spin nondegenerate materials such as graphene, it contains an additional Ising term in spin polarized graphene [12].…”

RKKY interaction in bilayer graphene

“…Equations (33) and (34) show that the interlayer RKKY interactions between magnetic impurities on different sublattices, J A 1 B 2 (R ij ) and…”

“…For example, quantum Hall effect, landau-level degeneracy and Berry phase [3,25,26], edge states [27], weak localization [28], Coulomb screening and collective excitations [29,30] in BLG are different from those in the ordinary 2DEG and also from those in SLG. The RKKY interaction in BLG can signalize this difference more [31,32,33]. In this paper we study the RKKY interaction in undoped BLG in the four-band model, by directly computing the Green's function in eigenvalues and eigenvectors representation.…”

Effect of the Rashba splitting on the RKKY interaction in topological-insulator thin films

“…4,5 Depending on the spin structure of the host material, different types of couplings can occur between magnetic adatoms via the RKKY interaction. While in spin-degenerate systems, such as graphene, [6][7][8][9] two localized magnetic impurities couple to each other in the form of isotropic collinear Heisenberg-like term, the anisotropic collinear Ising-like term with different coefficients in different spin-directions can be appeared in spin-polarized systems. 5,10 Moreover in materials with Rashba spin-orbit coupling [11][12][13] as well as materials with spin-valley coupling, 4,14,15 it has been shown that twisting RKKY interaction is possible by the anti-symmetric noncollinear Dzyaloshinskii-Moria-like term.…”