  A lateral Josephson junction in which the surface of a 3D topological
insulator serves as the weak link should support topologically protected
excitations related to Majorana fermions. The resulting $4\pi$-periodic
current-phase relationship could be detected under high-frequency excitation by
the suppression of odd Shapiro steps. Here, we demonstrate such devices through
the self-formation of a Pd-Te superconducting layer from a telluride
topological insulator, and observe suppressed first and third Shapiro steps.
Yet many of our devices, including ones where the Pd-Te layer is bolstered by
an additional Al layer, show no suppression of Shapiro steps. Though we rule
out the known trivial causes of suppressed Shapiro steps in our devices, our
results serve as a warning that the non-equilibrium physics of these systems
must be better understood before confidently claiming the observation of
Majorana states.

Mesoscale and Nanoscale Physics