Orbital-moment geometry and amplitude in rhombohedral graphene: a comparison of effective Hamiltonians

Abstract Magnetic imaging of rhombohedral graphene calls for a microscopic account of its orbital response. Using density-functional-derived Wannier Hamiltonians, we map the conduction-band orbital moment across thirteen films of three to fifteen layers at an imposed outer-layer potential difference of 100 meV and compare it with that of two model Hamiltonians. Between the endpoints, the moment-ring radius increases from 0.035 to 0.059 Å −1 and its peak, with one small reversal, from 19.5 to 53.9 μ B ; source tests at every thickness show incomplete carbon-p z support, so the series does not establish source-converged thickness trends. The local Berry-flux coefficient follows N/2π within 0.51 %, where N is the layer number. The chiral-N model reproduces the ring radius within 6 %, whereas its peak-moment ratio to the Wannier result grows overall from 1.9 to 8.4. The Slonczewski–Weiss–McClure model with bulk-graphite parameters gives radius ratios of 0.99–1.11 and amplitude ratios of 1.2–1.8. These comparisons distinguish the momentum scale from the interband response that sets the amplitude. All three Hamiltonians omit basis-position contributions to the orbital-moment operator, which could change both radius and amplitude; the comparison therefore establishes differences among the Hamiltonians, not absolute moments, and cannot calibrate a measurement.