Supermoiré domain-resolved effective Hamiltonians and valley topology in helical multilayer graphene

Abstract

Extending moiré graphene beyond twisted bilayers, helical trilayer graphene has shown topological bands and correlated states with reshaped moiré periodicity. Here we develop a theoretical framework for helical multilayer graphene to investigate its supermoiré relaxation and low-energy electronic structure. Using real-space lattice calculations, we find that relaxation reconstructs the system into locally periodic single-moiré domains, which provide the basis for a continuum description. Within each reconstructed domain, downfolding the first-shell model yields effective Hamiltonians near the Dirac points that reveal how the low-energy spectrum decomposes into folded Dirac sectors. We further evaluate the valley Chern numbers encoded in these effective Hamiltonians, obtaining domain-dependent and gate-tunable topological responses consistent with the lattice calculations. Our results establish a domain-resolved organizing principle for thicker helical graphene stacks, in which folded Dirac sectors partition the low-energy spectrum, while local stacking families determine the corresponding band character and topological response.

17 pages, 10 figures, 1 table