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Computation of bound states of semi-infinite matrix Hamiltonians with applications to edge states of two-dimensional materials. (arXiv:1810.07082v1 [physics.comp-ph])
来源于:arXiv
We present a novel numerical method for the computation of bound states of
semi-infinite matrix Hamiltonians which model electronic states localized at
edges of one and two-dimensional materials (edge states) in the tight-binding
limit. The na\"{i}ve approach fails: arbitrarily large finite truncations of
the Hamiltonian have spectrum which does not correspond to spectrum of the
semi-infinite problem (spectral pollution). Our method, which overcomes this
difficulty, is to accurately compute the Green's function of the semi-infinite
Hamiltonian by imposing an appropriate boundary condition at the semi-infinite
end; then, the spectral data is recovered via Riesz projection. We demonstrate
our method's effectiveness by a study of edge states at a graphene zig-zag edge
in the presence of defects, including atomic vacancies. Our method may also be
used to study states localized at domain wall-type edges in one and
two-dimensional materials where the edge Hamiltonian is infinite in both
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