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

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.

17 pages, 4 figures, discussion of results extended and references added, published version

References in corpus (12)

• Multiple types of topological fermions in transition metal silicides
• RKKY in half-filled bipartite lattices: graphene as an example
• Diluted Graphene Antiferromagnet
• RKKY Interaction in Graphene from Lattice Green's Function
• Magneto-optics of massless Kane fermions: Role of the flat band and unusual Berry phase
• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
• Dynamics of a quasiparticle in the $\alpha$-T${}_3$ model: Role of pseudospin polarization and transverse magnetic field on \textbf{\textit{zitterbewegung}}
• Magneto-optics of general pseudospin-s two-dimensional Dirac-Weyl fermions
• RKKY interaction in gapped or doped graphene
• Electronic states of pseudospin-1 fermions in $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• RKKY Interactions in Graphene Landau Levels
• RKKY interaction in graphene at finite temperature

Cited by in corpus (18)

• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Effect of magnetic field and chemical potential on the RKKY interaction in the $\alpha$-${\mathcal{T}}_3$ lattice
• Floquet engineering of topological phase transitions in quantum spin Hall $\alpha$-$T_3$ system
• Effect of magnetic field on the electronic properties of an $\alpha$-$T_3$ ring
• Thermal Transport Properties of Magnons on the $\alpha$-T${}_3$ Lattice
• Superfluidity of dipolar magnetoexcitons in doped double-layered $\alpha$-${\mathcal{T}}_3$ lattice in a strong magnetic field
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• Superfluidity of dipolar excitons in a double layer of $\alpha -T_3$ with a mass term
• RKKY interaction in one-dimensional flat-band lattices
• On the Sign of Fermion-Mediated Interactions
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian
• Spin-spin interaction mediated by chiral phonons
• RKKY quadratic and biquadratic spin-spin interactions in twisted bilayer graphene
• Quantum phase transitions on the hexagonal lattice
• Spinon mediation of witness spin dynamics in herbertsmithite
• Influence of flat bands on RKKY interaction: perspective of Fano defects