Intervalley Coherent Order in Rhombohedral Tetralayer Graphene on MoS_{2}

Multilayer rhombohedral graphene (RG) has recently emerged as a new, structurally simple flat-band system, which facilitates the exploration of interaction-driven correlation states with highly ordered electron arrangements. Despite a variety of many-body order behaviors observed in RG by transport measurements, the direct microscopic visualization of such correlated phases in real space is still lacking. Here, we show the discovery of a robust intervalley coherent order-a long-predicted ground state in RG-at 77 K in tetralayer RG placed on MoS_{2} via imaging atomic-scale spatial reconstruction of wave functions for correlated states. This state is visualized in ∼60% and ∼70% filled flat bands, where clear spectroscopic signatures of electronic correlations are observed, manifesting as a sqrt[3]×sqrt[3] reconstructed supercell on the graphene lattice. Surprisingly, such a sqrt[3]×sqrt[3] pattern is absent in hexagonal-boron-nitride-supported RG under the same experimental conditions. These findings, together with our Hartree-Fock mean-field calculations, suggest a spin-orbit proximity-induced robust intervalley coherent phase of interacting electrons in tetralayer RG. Our results provide microscopic insights into the correlated phases in RG multilayers and highlight the significant potential for realizing highly accessible collective phenomena through van der Waals proximity.