Herein, the energy dispersion relationship and the density of states of triangular and rectangular moiré patterns are investigated using a tight binding model. Their characteristics of Hofstadter butterflies under different magnetic fields are also examined. The results indicate that, by analyzing different moiré superlattices, Hofstadter butterflies arising from different moiré pattern structures are obtained, exhibiting considerable fractal characteristics and self-similarities. Moreover, it is also observed that under an alternating magnetic field, the redistribution of electronic states leads to a significant change in the density of states curve, and the Van Hove peak changes with the increase in magnetic field intensity. This study enriches the understanding of the electronic behavior of moiré systems, but it also provides multiple potential application directions for future technological development.

Graphene nanoribbons (GNRs) inherit the exceptional carrier mobility of graphene while offering tunable bandgaps, making them promising for high-performance optoelectronics. Here, we report a high-performance near-infrared photodetector based on a p-GNR/Al₂O₃/n-Si vertical heterojunction, where GNR is directly produced by dissociating double-walled carbon nanotubes (DWCNTs). The 10 nm Al₂O₃ interlayer serves as an effective barrier and passivation layer, suppressing dark current and enhancing interfacial charge separation. Under 1064 nm illumination, the device delivers outstanding performance. At −6 V bias, the responsivity and detectivity reach 159.55 A/W and 2.01 × 10¹² Jones, respectively. Notably, under zero-bias self-powered mode, it still achieves a high responsivity of 8.71 A/W, a detectivity of 1.15 × 10¹³ Jones, and a fast response time of 307.5 μs. These results fully validate the feasibility of GNR-based heterojunctions for high-performance optoelectronic devices and pave the way for their future integration into low-power, high-sensitivity photodetection systems and next-generation optoelectronic integrated circuits.