# Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

## TL;DR

This paper theoretically explores twisted double bilayer graphene, revealing that flat bands emerge under a displacement field, leading to ferromagnetic insulating states and spin-triplet superconductivity, with results aligning with recent experimental observations.

## Contribution

The study introduces a phase diagram for TDBLG showing flat band emergence under displacement fields and predicts spin-triplet superconductivity driven by ferromagnetic fluctuations.

## Key findings

- Flat bands appear only with a vertical displacement field D.
- Half-filled states are ferromagnetic insulators with valley Chern number C_v=2.
- Response to magnetic fields matches recent experimental data.

## Abstract

Two monolayers of graphene twisted by a small `magic' angle exhibit nearly flat bands leading to correlated electronic states and superconductivity, whose precise nature including possible broken symmetries, remain under debate. Here we theoretically study a related but different system with reduced symmetry - twisted {\em double} bilayer graphene (TDBLG), consisting of {\em two} Bernal stacked bilayer graphene sheets, twisted with respect to one another. Unlike the monolayer case, we show that isolated flat bands only appear on application of a vertical displacement field $D$. We construct a phase diagram as a function of twist angle and $D$, incorporating interactions via a Hartree-Fock approximation. At half filling, ferromagnetic insulators are stabilized, typically with valley Chern number $C_v=2$. Ferromagnetic fluctuations in the metallic state are argued to lead to spin triplet superconductivity from pairing between electrons in opposite valleys. Response of these states to a magnetic field applied either perpendicular or parallel to the graphene sheets is obtained, and found to compare favorably with a recent experiment. We highlight a novel orbital effect arising from in-plane fields that can exceed the Zeeman effect and plays an important role in interpreting experiments.