Delocalized Electronic States in Few-layer Black Phosphorus

To understand the interlayer coupling mechanism as illustrated by experimental band structures of ARPES in few-layer black phosphorus (BP), with and without electric fields, we performed density functional calculations and used a layer orbital tight binding model. We found a significant discrepancy between experimental and different theoretical results in the band split ratios. By tuning the weight of each layer in our tight binding model, we derived ratios that agree with experiments, and found that there is an intrinsic electric field and a charge delocalization in BP. Besides, we investigated how the effective mass change with layer number and sub-band index, and how they are tuned by electric field.