论文标题
蜂窝状晶格上相关拓扑绝缘子中的平流型铁磁性
Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice
论文作者
论文摘要
我们研究了在霍尼科姆晶格上的纺丝对称性haldane-hubbard模型的平坦频段铁磁阶段，用于平坦频段Z $ _2 $拓扑绝缘子的霍尼科姆晶格。这样的研究扩展了我们以前的[L. S. G. Leite和R. L. Doretto，物理。 Rev. B {\ Bf 104}，155129（2021）]，关于由Haldane-Hubbard模型描述的相关Chern绝缘子的平流型铁磁相。我们将其相应的非互动限制填充$ 1/4 $填充的拓扑哈伯德模型以及其较低的自由主义带的几乎平坦的频段限制。我们表明，可以定义与两种不同的自旋flip激发相关的玻色子算子，一种爆发（混合晶格激发）和第二个保留（同一晶格激发）的玻璃纤维算起与两个三角形三角形相关的索引。在琼脂化方案中，费米子模型被映射到有效的相互作用的玻色子模型中，该模型在谐波近似时考虑其二次项，以确定自旋波激发光谱。对于混合和相同的激发，我们发现自旋波频谱被覆盖并具有两个分支，下层和上部带之间的能量差距为$ k $ $ k $，而第一个布里尔属区域的$ k'$点。这种行为与相应的相关Chern绝缘子之一不同，Chern绝缘子的旋转波谱在第一个Brillouin区域的中心具有Goldstone模式，而Dirac点为$ K $和$ K'$点。我们还发现一些证据表明，同一晶格激发的自旋波段即使在完全平坦的频带限制中，在拓扑上也可能是不平凡的。
We study the flat-band ferromagnetic phase of a spinfull and time-reversal symmetric Haldane-Hubbard model on a honeycomb lattice within a bosonization formalism for flat-band Z$_2$ topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B {\bf 104}, 155129 (2021)] concerning the flat-band ferromagnetic phase of a correlated Chern insulator described by a Haldane-Hubbard model. We consider the topological Hubbard model at $1/4$ filling of its corresponding noninteracting limit and in the nearly flat band limit of its lower free-electronic bands. We show that it is possible to define boson operators associated with two distinct spin-flip excitations, one that changes (mixed-lattice excitations) and a second one that preserves (same-lattice excitations) the index related with the two triangular sublattices. Within the bosonization scheme, the fermionic model is mapped into an effective interacting boson model, whose quadratic term is considered at the harmonic approximation in order to determine the spin-wave excitation spectrum. For both mixed and same-lattice excitations, we find that the spin-wave spectrum is gapped and has two branches, with an energy gap between the lower and the upper bands at the $K$ and $K'$ points of the first Brillouin zone. Such a behavior is distinct from the one of the corresponding correlated Chern insulator, whose spin-wave spectrum has a Goldstone mode at the center of the first Brillouin zone and Dirac points at $K$ and $K'$ points. We also find some evidences that the spin-wave bands for the same-lattice excitations might be topologically nontrivial even in the completely flat band limit.
