Topological Chiral Superconductor with Spontaneous Vortices and Supercurrent in Twisted Bilayer Graphene

We present a study of d-wave superconductivity in twisted bilayer graphene within mean-field theory, and demonstrate new phenomena that arise due to the moire superlattice. In the d-wave pairing, the relative motion (RM) of two electrons in a Cooper pair can have either d₊ or d_- symmetry, which carry opposite angular momenta. Due to the enlarged moire superlattice, the center-of-mass motion (COMM) can also carry a finite angular momentum without breaking the moire periodicity. By matching the total angular momentum, which has contributions from both the RM and the COMM, d₊ and d_- RMs are intrinsically coupled in a way such that the COMM associated with one of the RMs has a spontaneous vortex-antivortex lattice configuration. Another new phenomenon is that the chiral d-wave state carries spontaneous bulk supercurrent. We also discuss the superconductivity gap structure. The chiral d-wave superconductors are gapped and also topological as characterized by quantized Chern number. Nematic d-wave superconductors, which could be stabilized when the six-fold rotational symmetry of the twisted bilayer graphene is broken, for example by uniaxial strain, are gapless with point nodes.