标题： 任意子去局域化转变出无序的 fractional quantum anomalous Hall 绝缘体 显示英文标题

标题： Anyon delocalization transitions out of a disordered FQAH insulator

摘要： 受分数量子反常霍尔（FQAH）效应实验发现的启发，我们在存在猝灭无序的情况下，发展了一种关于掺杂诱导的从$\nu = 2/3$晶格Jain态跃迁的理论。我们表明，无序对之前工作中描述的导电相的演化有很强的影响。电荷$2/3$任意子的去局域化通过直接的二阶跃迁导致一种手征拓扑超导体，对于具有长波调制的平滑随机势而言也是如此。纵向电阻在相关的量子临界点处有一个普适峰。接近跃迁时，我们证明超导基态是一种“异常涡旋玻璃（AVG）”，在外加磁场不存在的情况下被稳定。对于短波无序，这种跃迁通常分裂为三个不同的跃迁，并伴有中间的绝缘拓扑相。如果相反，电荷$1/3$任意子去局域化，则在低掺杂情况下，结果是$\rho_{xy} = h/e^2$的回溯整数量子霍尔态。在较高掺杂下，这会经历第二次跃迁进入费米液体金属。我们表明，这个框架为最近在近$\nu = 2/3$的扭曲MoTe$_2$中观察到的复杂相图提供了一个合理的解释，并讨论了可以更详细地测试我们理论的未来实验。 显示英文摘要

摘要： Motivated by the experimental discovery of the fractional quantum anomalous Hall (FQAH) effect, we develop a theory of doping-induced transitions out of the $\nu = 2/3$ lattice Jain state in the presence of quenched disorder. We show that disorder strongly affects the evolution into the conducting phases described in our previous work. The delocalization of charge $2/3$ anyons leads to a chiral topological superconductor through a direct second order transition for a smooth random potential with long-wavelength modulations. The longitudinal resistance has a universal peak at the associated quantum critical point. Close to the transition, we show that the superconducting ground state is an ``Anomalous Vortex Glass (AVG)'' stabilized in the absence of an external magnetic field. For short-wavelength disorder, this transition generically splits into three distinct ones with intermediate insulating topological phases. If instead, the charge $1/3$ anyon delocalizes, then at low doping the result is a Reentrant Integer Quantum Hall state with $\rho_{xy} = h/e^2$. At higher doping this undergoes a second transition to a Fermi liquid metal. We show that this framework provides a plausible explanation for the complex phase diagram recently observed in twisted MoTe$_2$ near $\nu = 2/3$ and discuss future experiments that can test our theory in more detail.