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i'm looking for some references (prefer books) or explanations as to how one couple electrons so an EM field in a second quantized formalism tight binding model.

from what i know, one need to replace the hopping parameter with the same parameter multiplied by an exponent of the line integral of the vector potential along the hopping path. this is called the peierls substitution. after that in order to find the current - one need to calculate the derivative of the Hamiltonian with respect to the vector potential.

Can someone refer me to a book where this formalism is explained, or maybe explain here? i actually need this for a work i'm doing. I know that this is the method to couple to an EM field and finding the resulted current but i don't really understand why.

thank you very much!

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# Coupling to an electric field in a tight binding model

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