  Zirconium pentatelluride ZrTe5 is a topological semimetal. The presence of a
temperature induced Lifshitz transition, in which the Fermi level goes from the
conduction band to the valence band with increasing temperature, provides
unique opportunities to study the interplay between Fermi-surface topology,
dynamics of Dirac fermions, and Berry curvature in one system. Here we present
a combined experimental and theoretical study and show that a low energy model
can be used to understand the complicated Hall response and large anomalous
Hall effect observed in ZrTe5 over a wide range of temperature and magnetic
field. We found that the anomalous Hall contribution dominates the Hall
response in a narrow temperature window around the Lifshitz transition, away
from which the orbital contribution dominates. Moreover, our results indicate
that a topological phase transition coexists with the Lifshitz transition. Our
model provides a unifying framework to understand the Hall effect in semimetals
with large Zeeman splitting and non-trivial topology.
