论文标题
在延伸范围跳跃的情况下，半迪拉克·克恩绝缘子的新型拓扑阶段
Novel topological phases of a semi-Dirac Chern insulator in presence of extended range hopping
论文作者
论文摘要
我们在蜂窝状晶格上研究了延长范围（第三个邻居）跳跃的蜂窝状晶格，研究了半dirac haldane模型的拓扑特性和拓扑相变。在没有第三个邻居跳跃的情况下，$ t_3 $，该系统展示了无间隙的电子光谱，其存在会在分散体中造成能量差距。但是，光谱差距的性质，即，无论是微不足道还是拓扑，都需要确定。我们发现答案取决于$ t_3 $的价值，以及它与破坏Sublattice对称性的现场电位的相互作用，即Semenoff Mass（$δ$）。为了阐明我们在拓扑阶段的发现，我们使用可用的参数空间演示了两种相图，其中一个相位显示在$δ$ -T_3 $平面中，另一个以更熟悉的$δ$ -UD $ -UCATION-ϕ $平面（$ ϕ $是Haldane Flux）。该相图描述了Chern绝缘裂片的存在，其中包括Chern Number $ \ pm2 $和$ \ pm1 $的某些值$ T_3 $，以及微不足道的绝缘区域（零Chern编号）。因此，有从一个拓扑结构到另一种拓扑结构的相变为特征是Chern数值的突然变化。为了支持拓扑阶段的存在，我们计算了带状几何形状中的反向传播手性边缘模式。最后，异常的霍尔电导率显示了与这些拓扑阶段相对应的$ e^2/h $或$ 2E^2/h $的高原。
We study topological properties and the topological phase transitions therein for a semi-Dirac Haldane model on a honeycomb lattice in presence of an extended range (third neighbour) hopping. While in the absence of a third neighbour hopping, $t_3$, the system exhibits gapless electronic spectrum, its presence creates an energy gap in the dispersion. However, the nature of the spectral gap, that is, whether it is trivial or topological needs to be ascertained. We find that the answer depends on the value of $t_3$, and its interplay with the value of the onsite potential that breaks the sublattice symmetry, namely, Semenoff mass ($Δ$). To elucidate our findings on the topological phases, we demonstrate two kinds of phase diagrams using the available parameter space, one in which the phases are shown in the $Δ$-$t_3$ plane, and the other one in a more familiar $Δ$-$ϕ$ plane ($ϕ$ being the Haldane flux). The phase diagrams depict the presence of Chern insulating lobes comprising of Chern numbers $\pm2$ and $\pm1$ for certain values of $t_3$, along with trivial insulating regions (zero Chern number). Thus there are phase transitions from one topological regime to another which are characterized by abrupt changes in the values of the Chern number. To support the existence of the topological phases, we compute the counter-propagating chiral edge modes in a ribbon geometry. Finally, the anomalous Hall conductivity shows plateaus either at $e^2/h$ or $2e^2/h$ corresponding to these topological phases.
