标题： 三维扭曲双层石墨烯上拓扑绝缘体的拓扑表面态 显示英文标题

标题： Topological Surface States of 3D Topological Insulator on Twisted Bilayer Graphene

摘要： 我们对Bi$_2$Se$_3$的拓扑表面态（TSS）进行了全面的理论研究，这是一种在扭曲双层石墨烯（tBG）上外延生长的三维拓扑绝缘体。 由tBG引起的莫尔势将TSS的狄拉克锥折叠到莫尔布里渊区（MBZ），导致小能隙打开、能带变平以及次级狄拉克点的潜在出现。 通过有效场论、对称性分析和高阶微扰理论，我们分析了共格和非共格扭转角度，揭示了周期系统中的显著能带结构重构以及非共格系统中的准周期效应。 这项工作为拓扑保护与莫尔调制之间的相互作用提供了深入的见解，并为设计新的拓扑相提供了一条途径。 显示英文摘要

摘要： We present a comprehensive theoretical study of the topological surface states (TSS) of Bi$_2$Se$_3$, a 3D topological insulator, epitaxially grown on twisted bilayer graphene (tBG). The moir\'e potential induced by tBG folds the TSS Dirac cone into the moir\'e Brillouin zone (MBZ), resulting in mini-gap openings, band flattening, and the potential emergence of secondary Dirac points. Using effective field theory, symmetry analysis, and higher-order perturbation theory, we analyze both commensurate and incommensurate twist angles, revealing significant band structure reconstruction in periodic systems and quasi-periodic effects in incommensurate ones. This work provides deep insights into the interplay between topological protection and moir\'e modulation, offering a pathway to engineer novel topological phases.