Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter by Abhijeet Alase

Author:Abhijeet Alase
Language: eng
Format: epub, pdf
ISBN: 9783030319601
Publisher: Springer International Publishing

They are found to be spanned by and , respectively, where

corresponding to the emergent solutions

The boundary matrix reads

Since we have assumed 𝜖≠ ± 2t, the boundary matrix has a non-trivial kernel only if 𝜖 = 0, in which case it is spanned by {α 1 = [1 0 0 0]T, α 2 = [0 0 1 0]T}. Therefore, the zero-energy eigenspace is spanned by

Since these solutions are perfectly localized on the two edges, they exist for any N > 2 (see also Fig. 3.3). Interestingly, the above states also appeared as solutions of the bulk equation at the singular energies 𝜖 = ±2t, and failed to satisfy the BCs at those values of energy. We do not know whether this fact is just a coincidence or has some deeper significance.

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