Moire folded helical states at the interfaces of heterostructures

TL;DR

The paper addresses how moiré engineering at graphene–topological insulator interfaces can amplify and reorganize proximity-induced spin–orbit coupling. Using a minimal two-leg moiré ladder with Rashba SOC, it shows that the moiré potential both lifts spin degeneracy and halves the effective spectral periodicity, while redistributing helicity across a dense miniband network. The emergence of Dirac-like miniband crossings and strong helicity fluctuations in the bare response demonstrates that moiré-modulated SOC can support relativistic quasiparticles and enhanced helical textures without external interactions. This work suggests moiré design as a practical route to realize and tune helical phases in van der Waals heterostructures.

Abstract

A minimal model of a graphene topological insulator heterostructure is considered, where a moire superlattice modulates the Rashba spin orbit interaction. In the spin degenerate, spin orbit free limit, the reduced Brillouin zone contains flat, spin degenerate moire minibands, with periodicity determined by superlattice folding. The inclusion of spin orbit interaction lifts the spin degeneracy and reduces the effective spectral periodicity by a factor of two. Through spin orbit interaction, the moire 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 moire pattern, it induces helicity fragmentation, in which the helicity weight is distributed across a dense manifold of moire 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 spin orbit interaction demonstrates that moire 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 moire engineering.

Figures (4)

• Figure 1: (a) Illustration of the moiré ladder system. (b) Band spectra in the EBZ of $H(k)$, of a spinless system at $\delta=1$ (upper panel), a spinless system at $\delta=\frac{19}{20}$ (middle panel) and of a spinful system with $\alpha=t$ at $\delta=\frac{19}{20}$ (lower panel). Without SOC, the spectrum consists of spin-degenerate moiré minibands with periodicity set by the superlattice reciprocal vector. With SOC ($\alpha=t$), spin degeneracy is lifted and multiple avoided crossings appear. The effective periodicity of the spectrum in the EBZ is reduced by a factor of two, reflecting the breaking of pure translational symmetry by momentum-odd Rashba SOC. (c) DOS at T=0 of a spinless system with $\delta=1$ (upper panel), a spinless system with $\delta=\frac{19}{20}$ (middle panel) and a spinful system $\alpha=t$ at $\delta=\frac{19}{20}$ (lower panel).
• Figure 2: Zoom out of the spectrum of the minibands in the RBZ (close to the fermi energy (E=0). (a,b) spectrum of the system at $\delta=\frac{19}{20}$ and $\alpha=t$ without (a) and with (b) SOC. (c,d) spectrum of the system at $\delta=\frac{17}{20}$ and $\alpha=t$ without (c) and with (d) SOC.
• Figure 3: (a) Helical spectral function of the system at $\delta=\frac{19}{20}$, $\alpha=t$ and $T=0$. (b) zoom out of the minibands spectrum close to the fermi energy (E=0) at $\delta=\frac{19}{20}$, $\alpha=t$. The colors of the minibands reflect their helicity weight. (c) Helicity current spectral function at $\delta=\frac{19}{20}$, $\alpha=t$ and $T=0$.
• Figure 4: (a-b) Lindhard susceptibility of the system with $\alpha=t$ and $T=0$ at (a) $\delta=\frac{19}{20}$ and (b) $\delta=\frac{17}{20}$. (c) Dynamical susceptibility of the helicity current operator of the system with $\alpha=t$ and $T=0.1$ at $\delta=\frac{17}{20}$.