Abstract
Recently, moir\'e superlattices have been found on the surface of topological insulators (TI) due to the rotational misalignment of topmost layers. In this work, we study the effects of moir\'e superlattices on the topological surface states using a continuum model of Dirac electrons moving in a periodic potential. Unlike twisted bilayer graphene, moir\'e surface states cannot host isolated bands due to their topological nature. Instead, we find (high-order) van Hove singularities (VHS) in the moir\'e band structure that give rise to divergent density of states (DOS) and enhance interaction effects. Due to spin-momentum locking in moir\'e 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.
Highlights
In recent years, moiresuperlattices have been studied extensively in various 2D van der Waals heterostructures exemplified by graphene and transition metal dichalcogenide (TMD) multilayers [1,2,3]
We find prominent van Hove singularities (VHS) in moiresurface states which give rise to divergent density of states (DOS)
We study the moiretopological insulator surface states using a continuum model of Dirac electrons moving in periodic potentials at moirescale
Summary
Moiresuperlattices have been studied extensively in various 2D van der Waals heterostructures exemplified by graphene and transition metal dichalcogenide (TMD) multilayers [1,2,3] These moiresystems exhibit a variety of remarkable electronic properties due to strong correlation effects in flat minibands. We further study interaction effects near (high-order) VHS enhanced by the divergent DOS [16,17,18,19]. We solve the gap equation for the superconducting critical temperature Tc in the presence of power-law divergent density of states, taking account of both electron-phonon interaction and Coulomb repulsion within the Anderson-Morel approximation [22] (Sec. III). We discuss several experimental platforms to search for moiresurface states and enhanced superconductivity
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