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?
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2$\begingroup$ 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. $\endgroup$– ProfMCommented Apr 5, 2021 at 7:19
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$\begingroup$ @ProfM I use wannier90 to fit the DFT data from VASP. From what Ive got, the tight binding matrix element mainly contain the intra-layer hopping term and the inter-layer hopping is not dominant. I want to study their edge state in higher atomic layer system. Due to the limitation of computational cost, I was suggested to use the tight binding matrix of lower atomic system to approximate the higher one without doing expensive DFT again. I have no idea how to modify the original tight binding matrix I got. Should I just expand the dimension of the matrix and copy the element of original matrix? $\endgroup$– JensenPangCommented Apr 5, 2021 at 9:51
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1$\begingroup$ 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. $\endgroup$– ProfMCommented Apr 5, 2021 at 10:23
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1$\begingroup$ @ProfM I think the two comments you have given would probably make for a good answer $\endgroup$– Tyberius ♦Commented Jan 14, 2022 at 17:16
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$\begingroup$ @ProfM I agree with Tyberius! What do you think Jensen? $\endgroup$– Nike Dattani - No Free TimeCommented Sep 6, 2022 at 19:36
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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.