Dirac versus Weyl Fermions in Topological Insulators: Adler-Bell-Jackiw Anomaly in Transport Phenomena

Dirac metals (gapless semiconductors) are believed to turn into Weyl metals when perturbations, which break either time reversal symmetry or inversion symmetry, are employed. However, no experimental evidence has been reported for the existence of Weyl fermions in three dimensions. Applying magnetic fields near the topological phase transition from a topological insulator to a band insulator in ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ we observe not only the weak antilocalization phenomenon in magnetoconductivity near zero magnetic fields ($Bl0.4\text{ }\text{ }\mathrm{T}$), but also its upturn above 0.4 T only for $E//B$. This ``incompatible'' coexistence between weak antilocalization and ``negative'' magnetoresistivity is attributed to the Adler-Bell-Jackiw anomaly (``topological'' $E\ifmmode\cdot\else\textperiodcentered\fi{}B$ term) in the presence of weak antilocalization corrections.