Mesoscopic conductance fluctuations and noise in disordered Majorana wires

Anderson localization at the boundary of a two-dimensional topological superconductor

“…In many aspects our analysis follows the simpler m = 0 case (disordered wire without protected modes) hence we refer the reader to Ref. [20] for the details of such a calculation. In the present Section we will particularly focus on the points that are specific for the topologically nontrivial m = 0 case.…”

“…Also, we will compute the shot noise power of quasiparticles which is also due to the channels at the interface. The case without protected modes (m = 0, corresponding to n L = n R in the aforementioned setup) is special and was extensively studied previously [8,19,20]. It can be implemented in a superconducting wire with broken time-reversal and spin-rotational symmetries and does not require an adjacent two-dimensional gapped bulk superconductor.…”

“…Critical state between these two gapped phases is not fully localized by disorder [7][8][9]24]. Instead it is characterized by subohmic scaling of the average conductance with the wire length g ∝ 1/ √ L. In our previous publication [20], we computed conductance variance and other higher transport moments for a disordered Majorana wire with many conducting channels fine-tuned to the critical regime. In the present paper we extend our research taking into account possible topologically protected modes, which can appear only if the studied 1D system is realized at an edge of a twodimensional topological superconductor.…”

“…Hence the sigma model with at least n = 2 replicas is required. Such a model was developed in our earlier work [20] for the topologically trivial wires with m = 0. In the present paper we generalize these model to include possible topologically protected modes in the case m = 0.…”

“…We briefly outline the algorithm described in detail in Ref. 20 and explain the modifications introduced by the WZW term. In Sec.…”