Topological and non-topological zero bias peaks in Majorana nanowires

Topological superconducting wires are predicted to support a localized Majorana bound state at each end. These Majorana states are particle-hole symmetric with a zero excitation energy. Their non-local properties and non-abelian braiding statistics, makes them potentially useful in topological quantum computation schemes. The present wave of interest is driven by a number of proposals that suggest ways of realizing and manipulating Majorana states in solid state systems. One proposal that stands out is the use of semiconductor nanowires with strong spin-orbit interaction that are placed in proximity to s-wave superconductors. Here Majorana manipulation require a mere series of gate operations. In light of these proposals, the experimental observations of zero-bias peaks in normal-metal superconductor tunnel junctions, may indicate the presence of a Majorana bound state. However, for the unambiguous identification of this topologically non trivial state, it is crucial to rule out alternative mechanisms for the zero-bias conductance peak in this apparatus. In the experimental setup the wires are terminated by gate induced potentials which are typically smooth functions of position. We  show that even in the topological trivial state such an adiabatic confinement can lead to a fermionic end state with an anomalously small energy. 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.