Nontrivial interplay of strong disorder and interactions in quantum spin-Hall insulators doped with dilute magnetic impurities

We investigate nonperturbatively the effect of a magnetic dopant impurity on the edge transport of a quantum spin Hall (QSH) insulator. We show that for a strongly coupled magnetic dopant located near the edge of a system, a pair of transmission anti-resonances appear. When the chemical potential is on resonance, interaction effects broaden the anti-resonance width with decreasing temperature, thus suppressing transport for both repulsive and moderately attractive interactions. Consequences for the recently observed QSH insulating phase of the $1$-T$^{\prime}$ of WTe$_2$ are briefly discussed.