  Topological insulator (TI) nanoribbons with proximity-induced
superconductivity are a promising platform for Majorana bound states (MBSs). In
this work, we consider a detailed modeling approach for a TI nanoribbon in
contact with a superconductor via its top surface, which induces a
superconducting gap in its surface-state spectrum. The system displays a rich
phase diagram with different numbers of end-localized MBSs as a function of
chemical potential and magnetic flux piercing the cross section of the ribbon.
These MBSs can be robust or fragile upon consideration of electrostatic
disorder. We simulate a tunneling spectroscopy setup to probe the different
topological phases of top-proximitized TI nanoribbons. Our simulation results
indicate that a top-proximitized TI nanoribbon is ideally suited for realizing
fully gapped topological superconductivity, in particular when the Fermi level
is pinned near the Dirac point. In this regime, the setup yields a single pair
of MBSs, well separated at opposite ends of the proximitized ribbon, which
gives rise to a robust quantized zero-bias conductance peak.

Mesoscale and Nanoscale Physics