Electrostatically stabilized surface flat bands in rhombohedral graphite at zero displacement field

Abstract: Rhombohedral (ABC-stacked) multilayer graphene hosts interaction-driven phases enabled by surface flat bands at large displacement fields. In thick flakes, however, strong screening suppresses internal electric fields, raising the question of whether a flat-band regime is accessible within the same experimental paradigm. Here, we show that self-consistent, nonlinear electrostatics provides a robust alternative mechanism: even in the absence of a displacement field, a nonuniform near-surface potential flattens the surface-band dispersion and enhances the density of states. In the strong-coupling limit, electrostatics drives the system toward uniform half-filling at each momentum, yielding an asymptotically flat surface band without any gating. At realistic interaction strengths, surface-band flatness is tuned by the proximal gate, with maximal flatness achieved at hole doping when the band is empty. Combining analytic arguments with fully self-consistent calculations in a realistic model, we map the resulting low-field regime and connect to finite $N!\sim! 6-15$ layered samples, providing a framework for analyzing the symmetry-broken phases observed in these systems. Our results motivate future experiments in large-$N$ devices and establish a low-field regime for exploring electrostatically induced flat-band physics.