ABC-stacked rhombohedral graphene multilayers exhibit a wide variety of electronic ground states characterized by broken isospin symmetry and superconductivity. Recently, indirect evidence of inter-valley coherent (IVC) order has been reported in rhombohedral trilayer graphene (RTG) [1], with possible implications for the origin of superconductivity [2]. In this talk I will present our recent work [3] on the first direct visualization of IVC order in RTG using scanning tunneling microscopy and spectroscopy. By tuning the chemical potential through the van-Hove singularity near the edge of the valence band, we observe a cascade of phase transitions associated with the formation of half- and quarter-metal states. Next, I will show that IVC phases, distinguished by an enlarged real space unit cell, are present near both the high- and low-density boundaries of the half-metal phase. I will discuss how we precisely reconstruct the IVC band structure through quasiparticle interference. Finally, I will present evidence of a novel IVC phase, an incommensurate IVC, that agrees with the recent prediction of an IVC-crystal phase [4]. This incommensurate order originates from the intrinsic annular Fermi surface of RTG. It introduces a spontaneously generated mini-Brillouin zone to the RTG band structure, in contrast to twisted systems where this feature is imposed by the stacking arrangement.
1. Intervalley coherence and intrinsic spin–orbit coupling in rhombohedral trilayer graphene.
Nat. Phys. 20, 1413–1420 (2024)
2. Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral
trilayer graphene. Nat. Commun. 13, 6013 (2022)
3. Visualizing incommensurate inter-valley coherent states in rhombohedral trilayer graphene.
arXiv:2411.11163 [cond-mat.mes-hall] (2024)
4. Incommensurate inter-valley coherent states in ABC graphene: collective modes and
superconductivity. arXiv:2408.10309v1 [cond-mat.str-el] (2024)