We calculate the edge current and its fluctuations, i.e., noise, in a two-dimensional topological superconductor using the $T$-matrix and the Green's function techniques. We show that the current is zero for nonchiral edge states and nonzero for chiral edge states, while the edge noise is nonzero whatever the chirality of the edge states. By applying our results to toy models with chiral edge states, we find that the noise is closely related to the Chern number. The edge noise is nonzero only when the Chern number is nonzero, and the bulk noise exhibits a peak each time the Chern number varies, meaning that there are strong current fluctuations when a topological phase transition occurs. Our results suggest that the bulk noise could be seen as a topological susceptibility. In the extended Qi-Wu-Zhang model, where an edge state is present even though the Chern number is zero, the edge noise no longer follows the same behavior as it does in the nonzero Chern number model. Instead, it is related to other topological invariants, such as the Zak phase.

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• Edge states
• Noise
• Superconductors
• Topological materials