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We consider magnetotransport on a helical edge of a quantum spin Hallinsulator, in the presence of bulk midgap states ``side-coupled" to the edge.In the presence of a magnetic field, the midgap levels are spin-split, andhybridization of these levels with the itinerant edge states leads tobackscattering, and the ensuing increase in the resistance. We show that thereis a singular cusp-like contribution to the positive magnetoresistance stemmingfrom resonant midgap states weakly coupled to the edge. The singular behaviorpersists for both coherent and incoherent edge transport regimes. We use thedeveloped theory to fit the experimental data for the magnetoresistance formonolayer WTe$_2$ at liquid helium temperatures. The results of the fittingsuggest that the cusp-like behavior of the resistance in weak magnetic fieldsobserved in experiments on monolayer WTe$_2$ with long edge channels mightindeed be explained by hybridization of the helical edge states with spin-splitbulk midgap states. In particular, the dependence of the magnetoresistance onthe direction of the external magnetic field is well described by theincoherent edge transport theory, at the same time being quite distinct fromthe one expected for a magnetic-field-induced edge gap.

Magnetotransport on quantum spin Hall edge coupled to bulk midgap states