Electronic Structure of Topological and Emergent Ground States in Rhombohedral Graphene

The presence of non-trivial topology where the electron wavefunction is protected from defects, in combination with strong electron correlations that give rise to emergent phenomena, form the basis for quantum materials with applications in information sciences. In two-dimensional van der Waals heterostructures, this is achieved by incorporating a twist between the constituent layers, which then is usually manifested in the electronic structure by forming a flat band at the Fermi level. However, the correlated phenomena in twisted systems are extremely sensitive to the angle disorder and strain, making them hard to achieve for experimental reproducibility. In this regard, graphene multilayers with rhombohedral or ABC stacking offers a different route to achieve flat bands. In this work, we have studied the flat band electronic structure of ABC stacked multilayer graphene as a function of thickness, temperature and doping via high resolution angle resolved photoemission spectroscopy (ARPES). Few-layer (4 - 120) graphene flakes are directly exfoliated on to highly conducting Si (100) substrates using blue tape. We then identified ABC stacked flakes via Raman spectroscopy measurements. The thickness of the flakes is determined via atomic force microscopy (AFM). Synchrotron-based micro-ARPES experiments revealed intense flat bands around the K point, close to Fermi level (E_F) along all azimuthal cuts. The presence of the flat bands over a large, measured photon energy range (44 -235 eV) confirms their surface origin. By measuring photon energy dependent (60-120 eV) Fermi surface maps, we verified the spiraling of Dirac nodal lines around the flat band. This bulk surface correspondence confirms the topological nature of the surface state. A careful study of the flat band in 20 nm thick flake revealed that it is both dispersive and split. The dispersion in thinner flakes (4 -5 layers) increases to 35 ± 10 meV, compared to thicker flakes (60-120 layers) where the surface state is flatter with a dispersion of 20 ± 10 meV. On the other hand, the splitting or the degenerate nature of the surface state present in thicker flakes disappears in thinner flakes, highlighting the presence of varying interlayer interactions. The degenerate nature of the surface state is revealed by measuring the dispersion spectra as a function of electron doping achieved via in-situ potassium dosing. At low doping, a gapless parabolic band is separated from the surface state; with further increase in doping, a gapped (35 – 80 meV) surface state is observed, demonstrating the emergence of interaction induced strongly correlated states. Our work provides critical insights in understanding the phase separated electronic structure of the surface state in rhombohedral graphite that is both correlated and topological in nature.