  With the recent discovery of Weyl semimetals, the phenomenon of negative
magnetoresistance (MR) is attracting renewed interest. While small negative MR
can occur due to the suppression of spin scattering or weak localization, large
negative MR is rare in materials, and when it happens, it is usually related to
magnetism. The large negative MR in Weyl semimetals is peculiar in that it is
unrelated to magnetism and comes from chiral anomaly. Here we report that there
is a new mechanism for large negative MR which is not related to magnetism but
is related to disorder. In the newly-synthesized bulk-insulating topological
insulator TlBi$_{0.15}$Sb$_{0.85}$Te$_2$, we observed gigantic negative MR
reaching 98% in 14 T at 10 K, which is unprecedented in a nonmagnetic system.
Supported by numerical simulations, we argue that this phenomenon is likely due
to the Zeeman effect on a barely percolating current path formed in the
disordered bulk. Since disorder can also lead to non-saturating linear MR in
Ag$_{2+\delta}$Se, the present finding suggests that disorder engineering in
narrow-gap systems is useful for realizing gigantic MR in both positive and
negative directions.
