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Background

So I've been working on making Hamiltonian Matrices for a graphene lattice and till now we've been working manually, I've attached a picture showing the matrices for a 2 by 2 Graphene Lattice where $t$ is the hopping parameter and $\epsilon$ is the on site energy. The empty terms are all zero

Matrices for 2 by 2 Graphene

Question

I've been working on a way to write a code which generalises these matrices by just taking the input parameters as the dimensions of the lattice, that is 2 by 2 or 4 by 4 or so. But I'm not sure how to set the conditions or how to convert the $A_i$ and $B_i$ basis to $2\times N_i \times N_i$ matrices. Where $N_i$ is the number of unit cells in any direction

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  • $\begingroup$ What do you mean by $2 \times N_i \times N_i$ matrix? And could you clarify your choice of unit cell? It should ordinarily contain two carbon atoms $\endgroup$
    – David_h
    Commented Sep 30 at 19:24
  • $\begingroup$ I suggest you identify what abstract objects encode the lattice and then use them to construct your lattice. $\endgroup$
    – zimmervi
    Commented Sep 30 at 19:33

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