Title: When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe$_2$ (and Other Systems) Show Chinese title

Title: 当阿贝尔分数拓扑绝缘体可能存在于扭曲的MoTe$_2$（及其他系统）中时

Abstract: Using comprehensive exact diagonalization calculations on $\theta \approx 3.7 ^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau level models also relevant for lower $\theta$, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at $\nu=1/3+1/3$, we investigate what features of the interaction destroy an FTI. For both pseudopotential interactions and realistic screened Coulomb interactions, we find that sufficient suppression of the short-range repulsion is needed for stabilizing an FTI. We then study $\theta \approx 3.7 ^{\circ}$ $t$MoTe$_2$ with realistic band-mixing and anisotropic non-local dielectric screening. Our finite-size calculations only find an FTI phase at $\nu=-4/3$ in the presence of a significant additional short-range attraction $g$ that acts to counter the Coulomb repulsion at short distances. We discuss how further finite-size drifts, dielectric engineering, Landau level character, and band-mixing effects may reduce the required value of $g$ closer towards the experimentally relevant conditions of $t$MoTe$_2$. Projective calculations into the $n=1$ Landau level, which resembles the second valence band of $\theta\simeq 2.1^\circ$ $t$MoTe$_2$, do not yield FTIs for any $g$, suggesting that FTIs at low-angle $t$MoTe$_2$ for $\nu=-8/3$ and $-10/3$ may be unlikely. While our study highlights the challenges, at least for the fillings considered, to obtaining an FTI with transport plateaus, even in large-angle $t$MoTe$_2$ where fractional Chern insulators are experimentally established, we also provide potential sample-engineering routes to improve the stability of FTI phases. Show Chinese abstract

Abstract: 利用对$\theta \approx 3.7 ^{\circ}$扭转双层 MoTe$_2$（$t$MoTe$_2$）的全面精确对角化计算，以及适用于更低$\theta$的理想朗道能级模型，我们提取了在实际情况下设计分数拓扑绝缘体（FTIs）的一般原则。 首先，在$\nu=1/3+1/3$的朗道能级设置下，我们研究了相互作用的哪些特性会破坏一个 FTI。 对于赝势相互作用和现实的屏蔽库仑相互作用，我们发现需要足够抑制短程排斥力才能稳定一个 FTI。 然后我们研究了带有现实带混合和各向异性非局域介电屏蔽的$\theta \approx 3.7 ^{\circ}$ $t$ MoTe$_2$。我们的有限尺寸计算仅发现在存在显著的额外短程吸引力$g$时，在$\nu=-4/3$处才出现FTI相，该吸引力的作用是抵消短距离的库仑排斥力。 我们讨论了进一步的有限尺寸漂移、介电工程、朗道能级特性以及能带混合效应如何可能使$g$的所需值更接近$t$MoTe$_2$的实验相关条件。 投影到$n=1$朗道能级的计算，该能级类似于$\theta\simeq 2.1^\circ$的第二价带 $t$MoTe$_2$，对于任何$g$都没有得到FTI（拓扑绝缘体），这表明在低角度 $t$MoTe$_2$对于$\nu=-8/3$和$-10/3$来说可能是不太可能的。 尽管我们的研究强调了实现FTI（ fractional topological insulator，分数拓扑绝缘体）时所面临的挑战，至少对于所考虑的填充情况，在大角度$t$MoTe$_2$中（其中分数陈绝缘体在实验上已被确立），即使如此，我们也提出了可能的样品工程路线以提高FTI相的稳定性。