Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach

TL;DR

This study investigates the pairing symmetry and vortex structures in superconducting twisted bilayer graphene using Bogoliubov-de Gennes equations, revealing phase transitions, spontaneous vortices, and the significance of long-range interactions.

Contribution

It provides a detailed microscopic analysis of pairing symmetries and vortex phenomena in twisted bilayer graphene, highlighting effects not captured by existing models.

Findings

Transition from mixed $d+id$ and $p+ip$ to $s+p+d$ phase with increasing pairing potential

Spontaneous vortex-antivortex lattices induced by twist in the $d+id$ and $p+ip$ phases

Superconducting gap remains uniform despite nonuniform order parameter in moiré cell

Abstract

We study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moir\'{e} 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 moir\'{e} 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.