Hamiltonian constant term

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I am reading an article on Arxiv about modelling the electron structure in a nanowire crystal: http://arxiv.org/abs/1511.08044
But I am having trouble understanding the hamiltonians (1) and (2).
In (1) what is the purpose of the term E_gap/2. Is that just a reference point for the energy or something?
In (2) why does the spin orbit term look like it does? In my world spin orbit is something like S⋅L, i.e. a coupling between the orbital angular momentum of the nucleus and the spin of the electrons. Is that what the terms describes?
 

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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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