  The geometric phase (Berry phase) of an electronic wave function is the
fundamental basis of the topological properties in solids. Modulating band
structure provides a tuning knob for the Berry phase, and in the extreme case
drives a topological phase transition. Despite the significant developments in
topological materials study, it remains a challenge to tune between different
topological phases while tracing the impact of the Berry phase on quantum
charge transport, in the same material. Here we report both in a
magnetotransport study of ZrTe5. By tuning the band structure with uniaxial
strain, we directly map a weak- to strong- topological phase transition through
a gapless Dirac semimetal phase via quantum oscillations. Moreover, we
demonstrate the impact of the strain-tunable spin-dependent Berry phase on the
Zeeman effect through the amplitude of the quantum oscillations. We show that
such a spin-dependent Berry phase, largely neglected in solid-state systems, is
critical in modeling quantum oscillations in Dirac bands in topological
materials.
