  Analogous to 2D layered transition metal dichalcogenides, the TlSe family of
1D chain materials with Zintl-type structure exhibits exotic phenomena under
high-pressure. In the present work, we have systematically investigated the
high-pressure behavior of TlInTe 2 using Raman spectroscopy, synchrotron X-ray
diffraction, and transport measurements, in combination with crystal structure
prediction (CSP) based on the evolutionary approach and first principles
calculations. We found that TlInTe$_2$ undergoes a pressure driven
semiconductor to semimetal transition at 4 GPa, followed by a superconducting
transition at 5.7 GPa (with Tc = 3.8 K) induced by a Lifshitz transition. The
Lifshitz transition is initiated by the appearance of new electron pockets on
the Fermi surface, which evolve with pressure and connect to the adjacent
electron pockets forming an umbrella shaped Fermi surface at the top and bottom
of the Brillouin zone. An unusual giant phonon softening (Ag mode) concomitant
with a V-shaped Tc behavior appears at 10-12 GPa as a result of the interaction
of optical phonons with the conduction electrons, resulting in Fano line shaped
asymmetry in Ag mode. A prominent Tc anomaly concurrent with the Ag mode
softening at 19-20 GPa is correlated to the semimetal to metal transition. The
CSP calculations reveal that these transitions are not accompanied by any
structural phase transitions up to the maximum pressure achieved, 33.5 GPa. Our
findings on TlInTe$_2$ open up a new platform to study a plethora of unexplored
high pressure novel phenomena in TlSe family induced by Lifshitz transition
(electronic driven), phonon softening and electron-phonon coupling.
