  Axions, hypothetical particles theorized to solve the strong CP-problem, are
presently being considered as strong candidates as cold dark matter
constituents. The signal power of resonant-based axion detectors, known as
haloscopes, is directly proportional to their quality factor $Q$. In this
paper, the impact of the use of superconductors in the performances of the
haloscopes is studied by evaluating the obtainable $Q$. In particular, the
surface resistance $R_s$ of NbTi, Nb$_3$Sn, YBa$_2$Cu$_3$O$_{7-\delta}$ and
FeSe$_{0.5}$Te$_{0.5}$ is computed in the frequency, magnetic field and
temperature ranges of interest, starting from the measured vortex motion
complex resistivity and screening lengths of these materials. From $R_s$ the
quality factor $Q$ of a cylindrical haloscope with copper conical bases and
superconductive lateral wall, operating with the TM$_{010}$ mode, is evaluated
and used to perform a comparison of the performances of the different
materials. Both YBa$_2$Cu$_3$O$_{7-\delta}$ and FeSe$_{0.5}$Te$_{0.5}$ are
shown to improve the measurement sensitivity by almost an order of magnitude
with respect to a whole Cu cavity, while NbTi is shown to be suitable only at
lower frequencies (<10 GHz). Nb$_3$Sn can give an intermediate improvement in
the whole spectrum of interest.
