Disorder effects on quantum transport and quantum phase transition in low-dimensional superconducting and topological systems

Disorder effects inevitably exist in realistic samples, manifesting in various physical properties. In this paper, we review the recent progress in understanding the disorder effects on quantum transport and quantum phase transition properties in low-dimensional superconducting and topological systems. As a consequence of the pronounced quantum fluctuation in low-dimensional systems, rare events drastically change the physical characteristics and underlying microscopic transport process in these systems, which are beyond the traditional paradigms. Associating with recent experimental observations, we emphasize the microscopic mechanism for disordered Ising superconductivity, the quantum Griffiths singularity of superconductor metal transition and the discrete scale invariance in topological materials.