Moiré-modulated $\hat{I}“$ valley in twisted bilayer and twisted double-bilayer MoTe${}_2$

Abstract

Twisted MoTe${}_2$ hosts intriguing correlated quantum phenomena including the fractional quantum anomalous Hall effect in twisted bilayer (t-BL) MoTe${}_2$ near 3.7${}^{\circ }$, which is sensitive to the twist angle and moiré superlattices. Here, we directly visualize the twist-angle-modulated electronic structure of t-BL and twisted double-bilayer (t-DBL) near this critical angle. We find that the moiré superlattice not only modifies the relative energy between $\hat{I}“$ and K valleys in t-BL MoTe${}_2$, but also strongly reconstructs the $\hat{I}“$ valley for both t-BL and t-DBL. Specifically, the deep $p_z$-derived band at $\hat{I}“$ exhibits a distinct splitting that systematically varies with increasing twist angle. Theoretical analysis suggests that this modulation arises from the twist-angle-dependent lattice relaxation, especially interfacial corrugations. Our work directly visualizes the moiré-modulated electronic structure and provides key spectroscopic information of lattice relaxation and interlayer interactions underlying the physics of twisted MoTe${}_2$.

7 pages, 5 figures