Condensed Matter Seminar: Visualizing Inter-Valley Coherent States in Rhombohedral Trilayer Graphene

Graphene heterostructures, in the presence of a superlattice potential induced by twist, have opened new avenues for exploring interaction-driven physics. In a parallel development, studies of rhombohedral trilayer graphene without a moiré superlattice have revealed an equally rich phase diagram, including interaction-driven ferromagnetic transitions and unconventional superconductivity. The enhanced interactions in these non-moiré systems arise from a band gap opened by a vertical displacement field and the associated high density of states featuring van Hove singularities (VHS). When the VHS are partially filled, a cascade of electronic phase transitions emerges. Recently, indirect evidence of inter-valley coherent (IVC) order has been reported in rhombohedral trilayer graphene, with potential implications for the origin of superconductivity. In this state, the electronic wave functions in the two valleys form a superposition characterized by a macroscopically coherent phase. In my talk, I will introduce the rhombohedral trilayer graphene system, its unique properties and correlated phase diagram, and describe how we probe it using scanning tunneling microscopy and spectroscopy. I will then present a direct visualization of the IVC order in rhombohedral trilayer graphene. We observe the reconstructed band structure and IVC states in momentum space through quasiparticle interference measurements, and in real space through direct imaging of surface charge density modulations and their evolution with energy, carrier density, and displacement field. I will discuss the nature of the observed phases and demonstrate that IVC phases represent a widespread ground state within graphene systems.