Tunable superconductivity and M\"obius Fermi surfaces in an inversion-symmetric twisted van der Waals heterostructure

TL;DR

This paper theoretically investigates a mirror-symmetric twisted trilayer graphene heterostructure, demonstrating tunable superconductivity and M"obius Fermi surfaces induced by spin-orbit coupling and displacement fields, with implications for topological phases.

Contribution

It introduces a novel heterostructure setup enabling control over spin-orbit effects, revealing complex superconducting phases and M"obius Fermi surfaces with potential experimental observability.

Findings

Superconducting pairing varies with displacement field D_0, showing phase transitions.

Spin textures exhibit vortices leading to M"obius Fermi surfaces.

Superconducting order inherits M"obius spin textures.

Abstract

We study theoretically a moir\'e superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows to switch on/off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field $D_0$, and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with $D_0$; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase transitions between competing superconducting phases. Second, we reveal that, with application of $D_0$, the spin-orbit-induced spin textures exhibit vortices which lead to "M\"obius fermi surfaces'' in the interior of the Brillouin zone: diabatic electron trajectories, which are predicted to dominate quantum oscillation experiments, require encircling the $\Gamma$ point twice, making their M\"obius nature directly observable. We further show that the superconducting order parameter inherits the unconventional, M\"obius spin textures. Our findings suggest that this system provides a promising experimental avenue for studying systematically the impact of spin-orbit coupling on the multitude of topological and correlated phases in near-magic-angle twisted trilayer graphene.