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.

arXiv comment17 pages, 4 figures, discussion of results extended and references added, published version

References in corpus (46)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Dirac fermions and flat bands in the ideal kagome metal FeSn
• Artificial flat band systems: from lattice models to experiments
• Aharonov-Bohm cages in two-dimensional structures
• Multiple types of topological fermions in transition metal silicides
• Experimental realization and characterization of an electronic Lieb lattice
• RKKY in half-filled bipartite lattices: graphene as an example
• Diluted Graphene Antiferromagnet
• From dia- to paramagnetic orbital susceptibility of Dirac cones
• Topological Origin of Equatorial Waves
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• RKKY Interaction in Graphene from Lattice Green's Function
• RKKY coupling in graphene
• RKKY interaction in graphene
• RKKY Interaction in Graphene Calculated Following Ruderman and Kittel
• Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
• Magnetic field induced localization in a two-dimensional superconducting wire network
• Magneto-optics of massless Kane fermions: Role of the flat band and unusual Berry phase
• Realization of Lieb Lattice in Covalent-organic Frameworks with Tunable Topology and Magnetism
• Analytical Expression for the RKKY Interaction in Doped Graphene
• Hall quantization and optical conductivity evolution with variable Berry phase in $\alpha$-$T_3$ model
• Magnetic properties of the $\alpha$-$T_3$ model: magneto-optical conductivity and the Hofstadter butterfly
• Phase Diagram of the Bose-Hubbard Model with T_3 symmetry
• RKKY interaction on the surface of three-dimensional Dirac semimetals
• Magnetotransport properties of the $\alpha$-T${}_3$ model
• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
• Valley-polarized magnetoconductivity and particle-hole symmetry breaking in a periodically modulated $\alpha$-${\mathcal{T}}_3$ lattice
• Frequency dependent magneto-optical conductivity in the generalized $\alpha -T_3$ model
• Quasiparticle interference on type-I and type-II Weyl semimetal surfaces: a review
• Unconventional quantum Hall effects in two-dimensional massive spin-1 fermion systems
• Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice
• 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
• Electronic states of pseudospin-1 fermions in dice lattice ribbons
• Fingerprints of tilted Dirac cones on the RKKY exchange interaction in 8-Pmmn Borophene
• Vortex correlations in a fully frustrated two-dimensional superconducting network
• Ruderman-Kittel-Kasuya-Yosida interaction in biased bilayer graphene
• RKKY interaction between adsorbed magnetic impurities in graphene: symmetry and strain effects
• RKKY interaction in gapped or doped graphene
• Gap-modulated doping effects on indirect exchange interaction between magnetic impurities in graphene
• Enhancement of thermoelectric performance of a nanoribbon made of alpha-${\mathcal{T}}_3$ lattice
• Coexistence of spin-1 fermion and Dirac fermion on the triangular kagome lattice
• 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

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• 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
• Magnetoplasmons for the $\alpha$-T${}_3$ model with filled Landau levels
• 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
• RKKY interaction in one-dimensional flat-band lattices
• Superfluidity of dipolar excitons in a double layer of $\alpha -T_3$ with a mass term
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• On the Sign of Fermion-Mediated Interactions
• Spin-spin interaction mediated by chiral phonons
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian
• 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