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Understanding possible mechanisms, which can lead to suppression of helicaledge transport in Quantum Spin Hall (QSH) systems, attracted huge attentionright after the first experiments revealing the fragility of the ballisticconductance. Despite the very intensive research and the abundance oftheoretical models, the fully consistent explanation of the experimentalresults is still lacking. We systematize various theories of helical transportwith the help of the spin conservation analysis which allows one to single outsetups with the ballistic conductance being robustly protected regardless ofthe electron backscattering. First, we briefly review different theories ofedge transport in the QSH samples with and without the spin axial symmetry ofthe electrons including those theoretical predictions which are not consistentwith the spin conservation analysis and, thus, call for a deeper study. Next,we illustrate the general approach by a detailed study of representativeexamples. One of them addresses the helical edge coupled to an array ofHeisenberg-interacting magnetic impurities (MIs) and demonstrates that theconductance remains ballistic even if the time-reversal symmetry on the edge is(locally) broken but the total spin is conserved. Another example focuses onthe effects of the space-fluctuating spin-orbit interaction on the QSH edge. Itreveals weakness of the protection in several cases, including, e.g., thepresence of either the U(1)-symmetric, though not fully isotropic, MIs orgeneric electron-electron interactions.

Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples