AI 中文总结
本文理论研究赝自旋-1 Dirac-Rashba系统中时间反演对称性破缺时的量子自旋霍尔相，发现其仍可存在，还揭示Rashba耦合诱导的量子反常霍尔相等多种拓扑相及相变，确立该系统的自旋分辨拓扑特性。
AI 中文摘要
量子自旋霍尔（QSH）相通常被认为受时间反演对称性（TRS）保护。本文从理论上研究了赝自旋-1费米子α-T₃系统在存在TRS破缺的铁磁交换场与不守恒自旋的Rashba自旋-轨道耦合时QSH相的演化。尽管TRS破缺，QSH相仍在有限参数范围内存在，其特征为受自旋能隙保护的非零投影自旋陈数C_σ（σ=↑,↓）。无Rashba耦合时，QSH相对α依赖的临界交换场保持鲁棒性。Rashba自旋-轨道耦合（SOC）通过驱动相变进入两种不同的量子反常霍尔（QAH）相，定性重塑了相图：无论α取值如何，均出现C=2相；而当α≠0,1时，会出现C=1相，进一步被识别为源自单个谷的谷极化QAH相。将磁化强度旋转至面内会打开一阶螺旋边缘态的能隙，产生二阶拓扑绝缘体（SOTI）相，该相在合适的有限几何结构中具有局域的角态。我们还识别出两种不同SOTI相之间的拓扑相变，其由交换场等于α时的纳米带边缘态介导。这些结果确立了高赝自旋系统中的自旋分辨拓扑，以及α-T₃晶格作为通过磁交换和自旋-轨道耦合设计与控制多种拓扑相的通用平台的作用。
英文摘要
The Quantum spin Hall (QSH) phase is conventionally understood to be protected by time-reversal symmetry (TRS). Here, we theoretically investigated the fate of the QSH phase in a pseudospin-1 fermionic $α-\mathcal{T}_3$ system in the presence of a TRS-breaking ferromagnetic exchange field and spin-nonconserving Rashba spin-orbit coupling. Despite broken TRS, the QSH phase survives over a finite parameter regime and is characterised by a non-zero projected spin-Chern number $C_σ(σ= \uparrow, \downarrow)$, protected by a spin-spectral gap. In the absence of Rashba coupling, the QSH phase remains robust up to an $α$-dependent critical exchange field. Rashba SOC qualitatively reshapes the phase diagram by driving transitions into two distinct quantum anomalous Hall (QAH) phases: a $C=2$ phase, irrespective of $α$-values, and a $C=1$ phase for $α\neq 0,1$, which is further identified as a valley-polarized QAH phase arising from a single valley. Rotating the magnetization to in-plane gaps out the first-order helical edge states and gives rise to second-order topological insulator (SOTI) phases that host localized corner states in suitable finite geometry. We further identify a topological phase transition between two different SOTI phases, mediated by nanoribbon edge states at an exchange field equal to $α$. These results establish spin-resolved topology in a higher pseudospin system as well as the $α-\mathcal{T}_3$ lattice as a versatile platform for engineering and controlling multiple topological phases through magnetic exchange and spin-orbit coupling.
