I have a 2D tight binding Hamiltonian now, Is there some methods to solve 1D nano ribbon edge state starting with 2D Hamiltonian?
Thanks a lot!
Maybe you can try to use periodic boundary conditions for a one dimensional lattice, like in carbon nanotubes, is it what you mean? You can read more on "Saito-Physical Properties of Carbon Nanotubes". I hope it helps.
As far as I understand your question, you need to calculate edge state of nanoribbon, which is described by a 2D tight-binding Hamiltonian. Probably this problem is effectievly 1D. Edge state is a state which is locolized in the edge, as I understand, so you should try to solve tight-binding equations with a boundary condition describing an exponential decay inside the ribbon.
You may use the recursion method (RM) for calculation the local density of electronic states (LDS) in tight-binding approximation. Possible, the edge LDS will be enough for your purposes. The RM is very computationally effective.
I used it in the 80s for calculations the local electronic structure for point and surface defects in 3D semiconductors and dielectrics. See, for example, [G. V. Gadijak et al. - Hydrogen adsorption on the silicon (001) surface and on a step on the (111) surface. Czech. J. Phys, 1985, V.35(1) 54-61] and other my full-text papers (using RM) in ResearchGates.
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