  Ordered assemblies of magnetic atoms on the surface of conventional
superconductors can be used to engineer topological superconducting phases and
realize Majorana fermion quasiparticles (MQPs) in a condensed matter setting.
Recent experiments have shown that chains of Fe atoms on Pb generically have
the required electronic characteristics to form a 1D topological superconductor
and have revealed spatially resolved signatures of localized MQPs at the ends
of such chains. Here we report higher resolution measurements of the same
atomic chain system performed using a dilution refrigerator scanning tunneling
microscope (STM). With significantly better energy resolution than previous
studies, we show that the zero bias peak (ZBP) in Fe chains has no detectable
splitting from hybridization with other states. The measurements also reveal
that the ZBP exhibits a distinctive 'double eye' spatial pattern on nanometer
length scales. Theoretically we show that this is a general consequence of STM
measurements of MQPs with substantial spectral weight in the superconducting
substrate, a conclusion further supported by measurements of Pb overlayers
deposited on top of the Fe chains. Finally, we report experiments performed
with superconducting tips in search of the particle-hole symmetric MQP
signature expected in such measurements.
