Topological antiferromagnetic spin-density-wave phase in an extended Kondo lattice model

Abstract

By using an extended mean-field theory we study the phase diagram of the topological Kondo lattice model on the honeycomb lattice at half-filling, in which the conduction electrons are described by the Haldane model. Besides the well-defined Kondo insulator and normal antiferromagnetic spindensity-wave (N-SDW) state, it is found that a novel and nontrivial topological antiferromagnetic SDW state (T-SDW) with a quantized Hall conductance is possible if the quasiparticle gap is dominated by the next-nearest neighbor hopping rather than the antiferromagnetic order. By analyzing the low-energy effective Chern-Simon action and the corresponding chiral edge-state, the T-SDW could be considered as a quantum anomalous Hall insulator with antiferromagnetic long-range order. This novel state is apparently beyond Landau-Ginzburg paradigm, which can be attributed to the interplay of quantum anomalous Hall effect and the subtle antiferromagnetic order in the Kondo lattice-like model. While the transition between the SDW states and the Kondo insulator is found to be conventional (a first order transition), the transition between the N-and T-SDWs is, however, a topological quantum phase transition. Interestingly, such topological quantum phase transition can be described by Dirac fermions coupled to a U (1) Chern-Simon gauge-field, which resembles the critical theory between bosonic integer quantum Hall phases and superfluid phase and also indicates such topological quantum phase transition may fall into the 3D-XY universal class. It is expected that the present work may shed light on the interplay between conduction electrons and the densely localized spins on the honeycomb lattice.

Hexagon Ising-Kondo lattice: An implication for intrinsic antiferromagnetic topological insulator

“…However, the previous theoretical researches about AFMTI state were based on either approximation method or numerical simulation. In this paper, we study the interplay between topology and magnetism with TIKL, which has never been studied in such an exactly analytical way, and the results can also cover many conclusions in standard topological Kondo lattice [34,40]. We hope this work could bring some new insights into TKI.…”

“…and is inferred by the checkerboard order parameter φ c = 1 N s j (−1) j q j [33,34]. Here, f (k) = e −ik x + 2e The main results at zero temperature are summarized in Fig.…”

“…Although previous studies have revealed the AFM ground state under interplay of topology and Kondo-like interaction [34], the resultant AFMTI is limited to the zero temperature situation. In this work we confirm that the AFMTI state do sustain at a considerable finite temperature region.…”

“…Discussion.−The coexistence of (symmetry-protected) topological order and AFM long-range order has already been predicted in weak coupling regime of topological Kondo insulator (TKI) by a mean-field calculation [34] and further been investigated by a dynamic mean-field approximation [40]. However, the previous theoretical researches about AFMTI state were based on either approximation method or numerical simulation.…”

$\mathcal{Z}_2$ classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator

“…Indeed, in some low-dimensional topological Kondo lattices, AF phases with non-trivial topologies have been verified theoretically. 35 These considerations motivate us to study the transition to AF phases in threedimensional (3D) TKI, to classify these AF states and search topologically protected AF phase, then further reveal the transition processes among AF states and various PM topological insulating (TI) phases.…”