Graphene may exhibit different topological phases as a result of proximity to different substrates. We study the effect of superconductivity in such systems using the effective Bogolyubov-de Gennes Hamiltonian with different superconducting pairing order parameters. We analyze the topological phase transition and symmetry class of the system in different parameter regimes. A particularly interesting situation occurs when nearest-neighbor spin-singlet superconducting pairing is present in phases of proximitized graphene that exhibit either inverted band or quantum spin Hall behavior. Both superconducting phases show similar characteristics in the low-energy range, including the appearance of robust edge states, and are neighboring phases across a transition that closes the quasiparticle gap as the chemical potential changes. Detailed construction and analysis of the existence and nature of edge states are presented in different system regimes.

中文翻译：

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石墨烯超导对对称性和自旋轨道耦合

石墨烯由于与不同基底的接近性而可能表现出不同的拓扑相。我们使用具有不同超导配对顺序参数的有效Bogolyubov-de Gennes哈密顿量研究此类系统中的超导效应。我们分析了在不同参数范围内系统的拓扑相变和对称性类别。当在显示反向带或量子自旋霍耳行为的邻近石墨烯相中存在最邻近的自旋单超导对时，会发生特别有趣的情况。这两个超导相在低能范围内都显示出相似的特性，包括出现稳健的边缘态，并且它们是跨跃的相邻相，随着化学势的变化，该跃迁闭合了准粒子间隙。