超导扭曲双层石墨烯中的成对对称性和自发涡旋-反涡旋晶格：Bogoliubov-de Gennes方法
Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach
摘要：
通过求解莫尔超晶胞中所有电子的Bogoliubov-de Gennes方程，研究了扭曲双层石墨烯中的超导配对对称性。随着对势的增加，体系通过一级相变从非拓扑的$d+id$和$p+ip$混合相演化到$s+p+d$相.在时间反演对称性破缺$d+id$和$p+ip$阶段，扭曲诱导了伴随自发超导电流的涡旋和反涡旋晶格。超导序参量在莫尔晶胞中是不均匀的。然而，局域态密度中的超导能隙在单胞中是相同的。现有的有效模型没有捕捉到混合$d+id$和$p+ip$相的扭转诱导涡和非拓扑性质。我们的研究结果表明，有效的模型的长程配对相互作用的重要性。
英文摘要：
We study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moiré supercells. With increasing the pairing potential, the system evolves from the mixed nontopological $d+id$ and $p+ip$ phase to the $s+p+d$ phase via the first-order phase transition. In the time-reversal symmetry breaking $d+id$ and $p+ip$ phase, vortex and antivortex lattices accompanying spontaneous supercurrent are induced by the twist. The superconducting order parameter is nonuniform in the moiré unit cell. Nevertheless, the superconducting gap in the local density of states is identical in the unit cell. The twist-induced vortices and nontopological nature of the mixed $d+id$ and $p+ip$ phase are not captured by the existing effective models. Our results suggest the importance of long-range pairing interaction for effective models.
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