Sinai Diffusion at Quasi-1D Topological Phase Transitions

Abstract

We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indexes. 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.

5 pages, 3 figures + 2 pages of Supplemental Material

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• Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain
• Local equilibrium properties of ultraslow diffusion in the Sinai model
• Disordered Graphene Ribbons as Topological Multicritical Systems
• Precise determination of critical points of topological phase transitions via shift current in two-dimensional inversion asymmetric insulators
• Topology of ultra-localized insulators and superconductors
• Two parameter scaling in the crossover from symmetry class BDI to AI
• Dynamics of Anderson localization in disordered wires
• Quantum lattice Boltzmann study of random-mass Dirac fermions in one dimension
• Quantum Critical Dynamics Induced by Topological Zero Modes