Moir\'e-modulated $\Gamma$ 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 moir\'e 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 moir\'e superlattice not only modifies the relative energy between $\Gamma$ and K valleys in t-BL MoTe$_2$, but also strongly reconstructs the $\Gamma$ valley for both t-BL and t-DBL. Specifically, the deep $p_z$-derived band at $\Gamma$ 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 moir\'e-modulated electronic structure and provides key spectroscopic information of lattice relaxation and interlayer interactions underlying the physics of twisted MoTe$_2$.