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

When normal metals (NMs) are attached to topological insulators or topological superconductors, the quantum states in these finite adjacent materials can intermix and affect the topological zero-energy edge state. To address this issue, we consider three prototype lattice models, namely a Su-Schrieffer-Heeger/NM, a Kitaev/NM, and a Chern insulator/NM. For all these junctions, we find that there exist trivial zero-energy states caused by fine-tuning the chemical potential in the NM that can percolate into the topological region, thus mimicking a topological state. Interestingly, these fine-tuned states cannot cross the true Majorana end modes of the Kitaev/NM model as protected by the particle-hole symmetry, but the crossing is allowed in the Su-Schrieffer-Heeger/NM due to breaking of the chiral symmetry. In addition, even in Chern insulators where the topological edge state self-generates a symmetry eigenvalue, such a fine-tuned zero-energy state can still occur. Our results indicate that when a topological material is attached to a metallic layer, one has to be cautious as to identify true topological edge states merely from their energy spectra and wave function profiles near the interface, since it may be obscured by these fine-tuned zero energy states.