Given a tight binding matrix of a thin film system with a few atomic layers, is it possible to construct a tight binding matrix of higher atomic layers thin film from the lower one? For example, I have a 4 atomic layers tight binding matrix from the fitting of a DFT calculation, is it possible to use this matrix and construct a 10 atomic layers thin film tight binding matrix?
Just to preserve ProfM's comments that seem to to answer the question:
In principle yes, but its accuracy will depend somehow on the specific features of your current TB model and what you want for the new one. For example, if you only have nearest neighbour hoppings between layers, then it should be relatively easy to increase the number of layers, whereas if you want hoppings between distant layers, then you may not have enough information. If you specify some more the details of your current model, I can provide a full answer.
In response to a comment about whether the TB matrix could be expanded simply by copying existing layers:
If the interlayer hopping is weak, then I would say it is reasonable to truncate it at say the first nearest neighbour. In this way, you should be able to stack together the TB model you have to increase the number of layers.