Chiral topological superconductivity in twisted bilayer and double bilayer graphene

TL;DR

This paper theoretically explores the emergence of chiral topological superconductivity in twisted bilayer and double bilayer graphene, revealing phase transitions and the influence of various parameters on topological states.

Contribution

It develops an effective model incorporating spin-triplet pairing to analyze topological phases in twisted graphene systems, including effects of trigonal warping.

Findings

Identification of topological phase transitions via Chern number calculations.

Phase diagrams showing the dependence on chemical potential, order parameter, and twist angle.

Analysis of gap-closing points and their role in topological transitions.

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 moir\'e 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 moir\'e 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 moir\'e materials, offering a route towards engineering exotic topological superconductivity with tunable parameters.