Intervalley coherence and intrinsic spin-orbit coupling in rhombohedral trilayer graphene

TL;DR

This study investigates the complex interplay of valley and spin degrees of freedom in rhombohedral trilayer graphene, revealing how intrinsic spin-orbit coupling influences its electronic phases and superconducting properties.

Contribution

It provides the first detailed experimental analysis of valley coherence, orbital ferromagnetism, and spin-orbit effects in rhombohedral trilayer graphene, including a quantitative estimate of spin-orbit coupling strength.

Findings

Identification of competition between valley imbalanced and intervalley coherent states.

Detection of a hybrid phase influenced by intrinsic spin-orbit coupling.

Quantitative estimate of spin-orbit coupling strength (~50 μeV).

Abstract

Rhombohedral graphene multilayers provide a clean and highly reproducible platform to explore the emergence of superconductivity and magnetism in a strongly interacting electron system. Here, we use electronic compressibility and local magnetometry to explore the phase diagram of this material class in unprecedented detail. We focus on rhombohedral trilayer in the quarter metal regime, where the electronic ground state is characterized by the occupation of a single spin and valley isospin flavor. Our measurements reveal a subtle competition between valley imbalanced (VI) orbital ferromagnets and intervalley coherent (IVC) states in which electron wave functions in the two momentum space valleys develop a macroscopically coherent relative phase. Contrasting the in-plane spin susceptibility of the IVC and VI phases reveals the influence of graphene's intrinsic spin-orbit coupling, which drives the emergence of a distinct correlated phase with hybrid VI and IVC character. Spin-orbit also suppresses the in-plane magnetic susceptibility of the VI phase, which allows us to extract the spin-orbit coupling strength of $\lambda \approx 50\mu$eV for our hexagonal boron nitride-encapsulated graphene system. We discuss the implications of finite spin-orbit coupling on the spin-triplet superconductors observed in both rhombohedral and twisted graphene multilayers.