Visualizing inter-valley coherent states in rhombohedral trilayer graphene

Graphene heterostructures in presence of a superlattice potential induced by twist have opened new avenues to study interaction-driven physics. In a parallel development, studies of rhombohedral trilayer graphene without a moire superlattice revealed an equally reach phase diagram including interaction-driven ferromagnetic transitions and unconventional superconductivity. The enhanced interaction in the non-moiré systems originates from a band gap induced by a vertical displacement field and the associated density of states that includes van Hove singularities (VHS). When these VHS are partially filled with electrons, a cascade of electronic phase transitions results. Recently, indirect evidence of inter-valley coherent (IVC) order has been reported in rhombohedral trilayer graphene, with possible 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 direct visualization of the IVC order in RTG. We observe the reconstructed band structure and IVC states in momentum space through quasiparticle interference measurements, and in real space by 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 are a widespread ground state within graphene systems