Abstract

Since the advent of time-reversal-invariant topological insulators, the generalization of topology concepts has led to the discovery of a wide range of topological states. These topological states may undergo topological phase transitions (TPTs) accompanied by discontinuous changes in topological invariants. In this Letter, by combining time- and angle-resolved photoemission spectroscopy measurements with first-principles calculations, we have demonstrated the existence of distinct TPTs in the unoccupied states above the Fermi level in the ${\mathit{M}}_{2}{\mathrm{Te}}_{2}\mathrm{P}$ ($M=\text{Ti}$, Zr, or Hf) family. These TPTs arise from the inversion of the transition metal $d$ and Te $p$ orbitals due to the enhancement of spin-orbit coupling and variation in crystal fields, as the transition metal changes from $3d$ to $4d$ and then to $5d$. Eventually, dual topological states are achieved in the $5d$ system ${\mathrm{Hf}}_{2}{\mathrm{Te}}_{2}\mathrm{P}$, where a type-III Dirac semimetal state coexists with a strong topological insulator state. Finally, we reveal a rapid relaxation process in the nonequilibrium population of the Dirac surface state due to the presence of an additional interband scattering channel in the bulk.