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

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Phenomena

Background:

• Multilayer rhombohedral graphene (RG) is a novel flat-band system for studying electron correlation states.
• Previous studies observed many-body order in RG via transport measurements, but lacked real-space microscopic visualization.
• Understanding correlated phases in RG is crucial for exploring emergent quantum phenomena.

Purpose of the Study:

• To microscopically visualize correlated electronic phases in tetralayer rhombohedral graphene.
• To identify and characterize the predicted intervalley coherent order in RG.
• To investigate the role of substrate interactions (MoS2 vs. hBN) on correlated states in RG.

Main Methods:

• Atomic-scale spatial reconstruction of wave functions using advanced imaging techniques.
• Spectroscopic analysis to identify signatures of electronic correlations.
• Hartree-Fock mean-field calculations for theoretical validation.

Main Results:

• Discovery of a robust intervalley coherent order in tetralayer RG on MoS2 at 77 K.
• Visualization of a sqrt[3]×sqrt[3] reconstructed supercell, indicating electronic correlations in filled flat bands.
• Absence of the sqrt[3]×sqrt[3] pattern in RG supported by hexagonal boron nitride (hBN).

Conclusions:

• The observed intervalley coherent order is likely induced by spin-orbit proximity effects from the MoS2 substrate.
• This finding provides the first direct microscopic evidence of correlated phases in RG.
• Van der Waals proximity engineering is highlighted as a powerful tool for realizing collective electronic phenomena in layered materials.