One-dimensional $p$-wave superconductors are known to harbor Majorana bound states at their ends. Superconducting wires with a finite width $W$ may have fermionic subgap states in addition to possible Majorana end states. While they do not necessarily inhibit the use of Majorana end states for topological computation, these subgap states can obscure the identification of a topological phase through a density-of-states measurement. We present two simple models to describe low-energy fermionic subgap states. If the wire's width $W$ is much smaller than the superconductor coherence length $\xi$, the relevant subgap states are localized near the ends of the wire and cluster near zero energy, whereas the lowest-energy subgap states are delocalized if $W\gtrsim \xi$. Notably, the energy of the lowest-lying fermionic subgap state (if present at all) has a maximum for $W\sim \xi$.

• Received 21 October 2011

DOI:https://doi.org/10.1103/PhysRevB.85.060507