Experimental verification of a temperature-induced topological phase transition in TlBiS2 and TlBiSe2

Temperature dependence of the band structure, as well as the spin-polarization on the topologically trivial insulator ${\mathrm{TlBiS}}₂$ and nontrivial insulator $\mathrm{Tl}\mathrm{Bi}{\mathrm{Se}}₂$, have been investigated by spin- and angle-resolved photoelectron spectroscopy. Despite the recent theoretical prediction [Phys. Rev. Lett. 117, 246401 (2016).], topological phase transition (trivial to nontrivial for ${\mathrm{TlBiS}}₂$, nontrivial to trivial for $\mathrm{Tl}\mathrm{Bi}{\mathrm{Se}}₂$) does not occur in the observed temperature ranges (from 50 to 400 K for ${\mathrm{TlBiS}}₂$, from 50 to 475 K for $\mathrm{Tl}\mathrm{Bi}{\mathrm{Se}}₂$). Our results indicate that the discrepancy between the theory and the experiment can be understood by considering the overestimation of lattice parameters and the effect of lattice expansion that is neglected in the previous theory. Although some spin-polarized states are observed in ${\mathrm{TlBiS}}₂$, it is probably due to the Rashba-like surface (resonant) states and not the topological surface states. On the other hand, the topological surface states in $\mathrm{Tl}\mathrm{Bi}{\mathrm{Se}}₂$ is very robust even at 400 K and the spin-polarized states can be used for the real spintronic devices in the large temperature range.