  Negative longitudinal magnetoresistance (NLMR) is shown to occur in
topological materials in the extreme quantum limit, when a magnetic field is
applied parallel to the excitation current. We perform pulsed and DC field
measurements on Pb1-xSnxSe epilayers where the topological state can be
chemically tuned. The NLMR is observed in the topological state, but is
suppressed and becomes positive when the system becomes trivial. In a
topological material, the lowest N=0 conduction Landau level disperses down in
energy as a function of increasing magnetic field, while the N=0 valence Landau
level disperses upwards. This anomalous behavior is shown to be responsible for
the observed NLMR. Our work provides an explanation of the outstanding question
of NLMR in topological insulators and establishes this effect as a possible
hallmark of bulk conduction in topological matter.
