We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indices. Focusing on the example of thermal transport in class D ("Majorana") quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations - a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.
Bibliographical noteFunding Information:
The research of A.K. was supported by National Science Foundation Grant No. DMR1306734.