A one-dimensional spin-orbit coupled nanowire with proximity-induced pairing
from a nearby s-wave superconductor may be in a topological nontrivial state,
in which it has a zero energy Majorana bound state at each end. We find that
the topological trivial phase may have fermionic end states with an
exponentially small energy, if the confinement potential at the wire's ends is
smooth. The possible existence of such near-zero energy levels implies that the
mere observation of a zero-bias peak in the tunneling conductance is not an
exclusive signature of a topological superconducting phase even in the ideal
clean single channel limit.Comment: 4 pages, 4 figure
