Vertical optical transitions of helical Majorana edge modes in topological superconductors

Abstract

The search for evidence of Majorana states on the edges of topological superconductors 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 topological superconductors contribute to the 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 charge current operator onto helical Majorana edge states leads to interbranch hybridization terms. The general form of this contribution under a tunable time-reversal breaking field is obtained, which is valid in the subgap low-frequency regime where the edge energy spectrum is linear. In comparison, the current operator for normal helical edge states, such as in quantum spin Hall insulators, does not cause interbranch 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 topological superconductors.

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