Emergent Moir\'e fringes in direct-grown quasicrystal

Quasicrystals represent a category of rarely structured solids that challenge traditional periodicity in crystal materials. Recent advancements in the synthesis of two-dimensional (2D) van der Waals materials have paved the way for exploring the unique physical properties of these systems. Here, we report on the synthesis of 2D quasicrystals featuring 30{\deg} alternating twist angles between multiple graphene layers, using chemical vapor deposition (CVD). Strikingly, we observed periodic Moir\'e patterns in the quasicrystal, a finding that has not been previously reported in traditional alloy-based quasicrystals. The Moir\'e periodicity, varying with the parity of the constituent layers, aligns with the theoretical predictions that suggest a stress cancellation mechanism in force. The emergence of Moir\'e fringes is attributed to the spontaneous mismatched lattice constant in the oriented graphene layers, proving the existence of atomic relaxation. This phenomenon, which has been largely understudied in graphene systems with large twist angles, has now been validated through our use of scanning transmission electron microscopy (STEM). Our CVD-grown Moir\'e quasicrystal provides an ideal platform for exploring the unusual physical properties that arise from Moir\'e periodicity within quasicrystals.