Moir\'e Folded Helical States at the Interfaces of Heterostructures

Abstract

A minimal model of a graphene--topological-insulator heterostructure is considered, where a moir\'e superlattice modulates the Rashba spin-orbit interaction (SOC). In the spin-degenerate, spin-orbit--free limit, the reduced Brillouin zone contains flat, spin-degenerate moir\'e minibands, with periodicity determined by superlattice folding. The inclusion of SOC lifts the spin degeneracy and reduces the effective spectral periodicity by a factor of two. Through SOC, the moir\'e potential entangles spin, sublattice, and leg degrees of freedom, reshaping the miniband structure in momentum space and generating emergent helicity spectral functions. As the Rashba coupling is renormalized by the moir\'e pattern, it induces helicity fragmentation, in which the helicity weight is distributed across a dense manifold of moir\'e minibands, forming an extended network of helicity-carrying states and significantly enhancing helicity fluctuations at the bare-response level. The emergence of Dirac-like miniband crossings at finite SOC demonstrates that moir\'e heterostructures can support relativistic quasiparticles through band reconstruction. This model provides a microscopic mechanism by which proximity-induced spin-orbit coupling can be amplified via moir\'e engineering.