1：Experimental Design and Method Selection:

GaN nanowires were grown by plasma-assisted molecular beam epitaxy (PA-MBE) on various substrates including AlN/Si(111), SiN/Si(111), SiO2/Si(100), and graphene/SiO2/Si(100). The growth temperature and V/III ratio were optimized for each substrate to achieve comparable morphologies. Steady-state and time-resolved photoluminescence (PL) measurements were conducted at low temperatures (5-10 K) to analyze optical properties.

2：0). The growth temperature and V/III ratio were optimized for each substrate to achieve comparable morphologies. Steady-state and time-resolved photoluminescence (PL) measurements were conducted at low temperatures (5-10 K) to analyze optical properties. Sample Selection and Data Sources:

2. Sample Selection and Data Sources: Substrates were prepared with specific treatments (e.g., AlN buffer layer deposition, nitridation of Si, dry oxidation for SiO2). Graphene was transferred to SiO2/Si substrates using a poly(methyl methacrylate) (PMMA)-assisted method.

3：2). Graphene was transferred to SiO2/Si substrates using a poly(methyl methacrylate) (PMMA)-assisted method. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Equipment includes a RIBER Compact 12 MBE system with an RF plasma N source, optical pyrometer, reflection high-energy electron diffraction (RHEED), scanning electron microscopy (SEM), micro-photoluminescence (μPL) setups with lasers (244 nm Ar++ laser, 325 nm laser, Ti-sapphire laser with third harmonic generation at 266 nm), spectrometers with gratings (1200 lines/mm, 2400 lines/mm, 1800 lines/mm), charge-coupled device (CCD) detectors, streak camera, and Raman spectrometer (inVia Micro Raman spectrometer with 532 nm laser). Materials include GaN, graphene, SiO2, Si, AlN, PMMA, acetone, isopropyl alcohol, and various chemicals for etching and transfer.

4：Experimental Procedures and Operational Workflow:

Substrates were prepared and loaded into the MBE reactor. Growth conditions (temperature, V/III ratio, time) were set based on substrate type. After growth, samples were characterized using SEM for morphology, μPL for steady-state luminescence, time-resolved PL for dynamics, and Raman spectroscopy for graphene quality. Specific procedures include temperature calibration using RHEED, plasma operation at

5：57 sccm N2 flow and 400 W RF power, and excitation with lasers at various wavelengths and powers. Data Analysis Methods:

PL spectra were analyzed for peak positions, full width at half maximum (FWHM), and decay times using exponential fits. Statistical analysis of NW diameters was performed from SEM images. Raman spectra were used to confirm graphene layer number and quality.