Recently, moiré superlattices have been found on the surface of topological insulators due to the rotational misalignment of topmost layers. In this work, we study the effects of moiré superlattices on the topological surface states using a continuum model of Dirac electrons moving in a periodic potential. Unlike twisted bilayer graphene, moiré surface states cannot host isolated bands due to their topological nature. Instead, we find (high-order) van Hove singularities (VHS) in the moiré band structure that give rise to divergent density of states (DOS) and enhance interaction effects. Because of spin-momentum locking in moiré surface states, possible interaction channels are limited. In the presence of phonon mediated attraction, superconductivity is strongly enhanced by the power-law divergent DOS at high-order VHS. The transition temperature $T_c$ exhibits a power-law dependence on the retarded electron-phonon interaction strength ${\lambda }^{*}$. This enhancement is found to be robust under various perturbations from the high-order VHS.

中文翻译：

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莫尔表面状态和拓扑绝缘体中增强的超导性

最近，由于最顶层的旋转未对准，在拓扑绝缘体的表面上发现了莫尔超晶格。在这项工作中，我们使用狄拉克电子在周期性电势中移动的连续模型来研究莫尔超晶格对拓扑表面状态的影响。与扭曲的双层石墨烯不同，由于其拓扑性质，莫尔表面状态不能容纳孤立的带。取而代之的是，我们在莫尔带结构中发现（高阶）范霍夫奇异点（VHS），这会引起发散的态密度（DOS）并增强相互作用效果。由于旋转动量锁定在莫尔表面状态，因此可能的相互作用通道受到限制。在声子介导的吸引力的存在下，高阶VHS上的幂律发散DOS极大地增强了超导性。转变温度${Ť}_C$表现出幂律对延迟的电子-声子相互作用强度的依赖性${\lambda }^{*}$。发现这种增强在来自高阶VHS的各种扰动下具有鲁棒性。