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arXiv 2310.09415cond-mat.mtrl-sci
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双层$α-\mathcal{T}3$晶格中近平带的拓扑性质

Topological properties of nearly flat bands in bilayer $α-\mathcal{T}3$ lattice

Puspita Parui, Sovan Ghosh, Bheema Lingam Chittari

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AI总结：

本研究针对双层$α-\mathcal{T}_3$晶格，通过紧束缚方法分析Haldane通量对其能带拓扑的调控，揭示了参数$α$诱导的拓扑相变规律及陈数演化特征。

摘要：

我们采用紧束缚形式，研究了Haldane通量在双层$α-\mathcal{T}_3$晶格系统中的作用，同时考虑了可能存在的非等价、共格堆叠构型。双层$α-\mathcal{T}_3$晶格的单胞包含六个子晶格，其能谱由六条能带组成。在无Haldane通量的情况下，价带和导带的两个狄拉克点处均存在三重能带交叉。在循环堆叠的双层$α-\mathcal{T}_3$晶格系统中引入Haldane通量后，所有六条能带发生分离，其中包括两条低能、呈波纹状的近平带，且每条能带都被赋予非零陈数，使系统具有拓扑性。我们证明，通过调节每层中带标度参数$α$的子晶格间跃迁强度，可以诱导拓扑演化。在陈绝缘相的骰子晶格极限（$α=1$）下，从低能到高能的三对能带的陈数分别为$\pm2$、$\pm3$和$\pm1$。有趣的是，参数$α$的连续变化会通过两条低能带之间的能带交叉触发拓扑相变。这些交叉在导带和价带中发生的数值不同，且进一步依赖于次近邻（NNN）跃迁强度。在相变点，两条较低导带和价带的陈数分别从$\pm2$不连续变为$\pm5$、从$\pm3$不连续变为$0$，而第三条能带的陈数保持不变。

英文摘要：

We study the effect of Haldane flux in the bilayer $α$-$\mathcal{T}_3$ lattice system, considering possible non-equivalent, commensurate stacking configurations with a tight-binding formalism. The bilayer $α$-$\mathcal{T}_3$ lattice comprises six sublattices in a unit cell, and its spectrum consists of six bands. In the absence of Haldane flux, threefold band crossings occur at the two Dirac points for both valence and conduction bands. The introduction of Haldane flux in a cyclically stacked bilayer $α$-$\mathcal{T}_3$ lattice system separates all six bands, including two low-energy, corrugated nearly flat bands, and assigns non-zero Chern numbers to each band, rendering the system topological. We demonstrate that the topological evolution can be induced by modifying the hopping strength between sublattices with the scaling parameter $α$ in each layer. In the dice lattice limit ($α= 1$) of the Chern-insulating phase, the Chern numbers of the three pairs of bands, from low energy to higher energies, are $\pm 2$, $\pm 3$, and $\pm 1$. Interestingly, a continuous change in the parameter $α$ triggers a topological phase transition through band crossings between the two lower energy bands. These crossings occur at different values for the conduction and valence bands and depend further on the next nearest neighbor (NNN) hopping strength. At the transition point, the Chern numbers of the two lower conduction and valence bands change discontinuously from $\pm 2$ to $\pm 5$ and $\pm 3$ to $0$, respectively, while leaving the Chern number of the third band intact.

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