Chiral topological superconductivity in twisted bilayer and double bilayer graphene

Abstract

We present a theoretical investigation of the emergence of chiral topological superconductivity in small-angle twisted bilayer graphene (tBLG) and twisted double bilayer graphene (tDBLG). Using the low-energy continuum model and incorporating spin-triplet $p_{x}+i p_{y}$ pairing in each graphene layer, we construct the effective models for both tBLG and tDBLG with superconductivity. By varying the chemical potential, superconducting order parameter, and twist angle, we explore the emergence of topological superconducting phases via the calculation of Chern numbers. Our phase diagrams for tBLG and tDBLG (both AB-AB and AB-BA stackings) reveal distinct topological transitions, which are consistently marked by bulk gap-closing points. To gain further insight, we analyze the evolution of Chern numbers by tracking the number and location of gap closings within the moiré Brillouin zone. Additionally, we illustrate representative squared amplitude of Bloch states corresponding to different topological phases. In the later part of our study, the effect of trigonal warping on the topological superconducting properties is also discussed. Beyond the quantitative results, our study highlights how the interplay between moiré band structure and unconventional pairing symmetries enriches the landscape of possible superconducting states in twisted graphene systems. The framework developed here may also be extended to other multilayer moiré materials, offering a route towards engineering exotic topological superconductivity with tunable parameters.