The survival of topological signatures in the presence of average symmetries

The robust properties in topological states of matter under the effect of disorders is of great theoretical as well as experimental interests. One focus is on the disorders breaking either spatial symmetry or non-spatial symmetry (e.g., time-reversal, particle-hole and chiral symmetry) but restoring it on average. In this work, we consider a quasi-one-dimensional topological superconductor in the presence of disorders preserving average time-reversal symmetry or mirror symmetry. By calculating the transport signatures of multi-chain Kitaev and Majorana models, we show that the survival of the edge modes depends on the form of the disorders.