Incommensurate Moir\'e Stacking and Landau Quantization Without External Magnetic Field in Turbostratic Graphene

Abstract

Turbostratic multilayer graphene, composed of randomly twisted and stacked graphene sheets, offers a naturally disordered yet tunable platform for exploring moir\'e physics beyond tedious artificial stacking. Using scanning tunneling microscopy/spectroscopy (STM/STS) and Raman analysis, we uncover a wide distribution of twist angles and stacking configurations spontaneously formed across large-area turbostratic films. In several regions, we identify overlapping incommensurate moir\'e patterns consistent with locally chiral trilayer stacking. We observe van Hove singularities and reconstructed Dirac-like spectra whose angle dependence supports strong interlayer electronic coherence. In the highly strained trilayered regions, we observe peaks in the local density-of states with characteristic scaling of the quantized Landau levels strikingly even in the absence of a magnetic field. They arise from the strain-induced pseudo-magnetic fields (~ 26 T), making turbostratic graphene a single natural platform to explore the physics of moir\'e structures as well as of the pseudo-electromagnetic fields.