Displacement-field-tunable superconductivity in an inversion-symmetric twisted van der Waals heterostructure

TL;DR

This study explores how displacement fields and induced spin-orbit coupling affect superconductivity in inversion-symmetric twisted trilayer graphene, revealing tunable superconducting states through symmetry and electronic structure analysis.

Contribution

It provides a detailed analysis of the interplay between spin-orbit coupling, displacement fields, and superconductivity in twisted trilayer graphene, highlighting the tunability of superconducting order parameters.

Findings

Displacement field breaks inversion symmetry and induces spin-splitting.

Superconducting order parameters evolve with spin-orbit coupling and displacement field.

Symmetry analysis clarifies the influence of external fields on superconductivity.

Abstract

We investigate the superconducting properties of inversion-symmetric twisted trilayer graphene by considering different parent states, including spin-singlet, triplet, and SO(4) degenerate states, with or without nodal points. By placing transition metal dichalcogenide layers above and below twisted trilayer graphene, spin-orbit coupling is induced in TTLG and, due to inversion symmetry, the spin-orbit coupling does not spin-split the bands. The application of a displacement field ($D_0$) breaks the inversion symmetry and creates spin-splitting. We analyze the evolution of the superconducting order parameters in response to the combined spin-orbit coupling and $D_0$-induced spin-splitting. Utilizing symmetry analysis combined with both a direct numerical evaluation and a complementary analytical study of the gap equation, we provide a comprehensive understanding of the influence of spin-orbit coupling and $D_0$ on superconductivity. These results contribute to a better understanding of the superconducting order in twisted trilayer graphene.