Proximity-induced zero-energy states indistinguishable from topological edge states

When normal metals (NMs) are attached to topological insulators or superconductors, it is conceivable that the quantum states in these finite adjacent materials can intermix. In this case---and because NM usually does not possess same symmetry as material---it pertinent ask whether zero-energy edge layer affected by presence of NM. To address issue, we consider three prototype systems simulated tight-binding models, namely a Su-Schrieffer-Heeger/NM, Kitaev/NM, and Chern insulator/NM. For all junctions investigated, find there exist trivial ``fine-tuned'' percolate into region, thus mimicking state. These created fine-tuning chemical potential such some cross zero energy; they occur even when material topologically phase, over large region phase diagram. Interestingly, true Majorana end modes Kitaev/NM model cannot be crossed any state, metal case break particle-hole symmetry. On other hand, chiral Su-Schrieffer-Heeger chain broken NM, crossings allowed. addition, do preserve nonspatial symmetries, but state self-generates eigenvalue, fine-tuned still occur. Our results indicate metallic layer, one has cautious identify merely from their energy spectra wave function profiles near interface.