  In light of recent proposals to realize a topological superconductor on the
surface of strong topological insulators, we study impurity and vortex
scattering in two dimensional topological superconductivity. We develop a
theory of quasiparticle interference in a model of the surface of a three
dimensional strong topological insulator with a pairing term added. We consider
a variety of different scatterers, including magnetic and nonmagnetic impurity
as well as a local pairing order parameter suppression associated with the
presence of a vortex core. Similar to the case of a surface of a three
dimensional topological insulator without pairing, our results for non-magnetic
impurity can be explained by the absence of back scattering, as expected for a
Dirac cone structure. In the superconducting case, doping away from the Dirac
point leads to a doubling of the contours of constant energy. This is in
contrast to the unpaired case where the chemical potential simply adds to the
bias voltage and shifts the energy. This doubling of contours results in
multiplying the number of possible scattering processes in each energy.
Interestingly, we find that some processes are dominant in the impurity case
while others are dominant in the vortex case. Moreover, the two types of
processes lead to a different dependence on the chemical potential.
