  Topological insulators are characterized by spin-momentum-locked massless
surface states which are robust under various perturbations. Manipulating such
surface states is a topic of vigorous research, as a possible route for the
realization of emergent many-body physics in topological systems. Thus far,
time-reversal symmetry breaking via Coulomb and magnetic perturbations has been
a dominant approach for the tuning of topological states. However, the effect
of the structural degrees of freedom on quasi-particle dynamics in topological
materials remains elusive. In this work, we demonstrate a transition in HfTe5
between distinct topological phases as a function of either Te vacancy
concentration or applied strain; these phases are characterized theoretically
as a transition from strong to weak topological insulator and experimentally by
a transition from sharp surface states and Dirac crossing to a
Fermi-liquid-like quasiparticle state in which these surface-localized features
are heavily suppressed. Although vacancies can result in various consequences
such as scattering, doping, and structural distortions, we show that changes in
the lattice constants play the foremost role in determining the electronic
structure, self-energy, and topological states of HfTe5. Our results
demonstrate the possibility of using both defect chemistry and strain as
control parameters for topological phase transitions and associated many-body
physics.
