  The search for evidence of Majorana states on the edges of topological
superconductors (TSCs) is challenging due to the difficulty of detecting such
charge-neutral electronic quasiparticles. Local microwave spectroscopy has been
shown to be a possible method to detect propagating Majorana modes, where a
spatially focused light beam must be used. Here, we show that helical Majorana
modes in TSCs allow inter-band transitions and thus contribute to optical
conductivity under a spatially uniform light. The existence of such a signal
requires the system to break certain symmetries so that the projection of the
charge current operator onto helical Majorana edge states leads to inter-band
hybridization terms. The general form of this contribution under a tunable
time-reversal breaking field is derived, which is valid in the sub-gap
low-frequency regime where the edge energy spectrum is linear, and numerical
results are obtained in three TSC models, showing remarkable consistency with
the analytical prediction. In comparison, the current operator for normal
helical edge states, such as in quantum spin Hall insulators, does not cause
inter-band transitions and the related optical conductivity vanishes unless the
time-reversal symmetry is broken. Our results may help guide feasible
experiments to provide evidence of Majorana edge modes in TSCs.
