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The iron chalcogenides have been proved to be intrinsic topologicalsuperconductors to implement quantum computation because of their uniqueelectronic structures. The topologically nontrivial surface states ofFeTe$_{0.5}$Se$_{0.5}$ have been predicted by several calculations and thenconfirmed by high-resolution photoemission and scanning tunneling experiments.However, so far, the shreds of the electrical transport evidence fortopological surface states are still in absence. By carrying out electricaltransport experiments, we observe a topological transition with a nonlinearHall conductivity and simultaneous linear magnetoresistance near thesuperconducting transition temperature. Furthermore, we observe a sign reversalof the Hall coefficient accompanied by a concurrently softening of the${A}_{1g}$ phonon mode at about 40 K, indicating a nematic transition. Thesynchronized phonon softening with nematicity manifests an enhanced fluctuationstate through spin-phonon interaction. Our results solidly corroborate thetopological surface states of FeTe$_{0.5}$Se$_{0.5}$ and provide anunderstanding of the mechanism of the superconductivity in iron chalcogenides.

Transport evidence for the surface state and spin-phonon interaction in FeTe$_{0.5}$Se$_{0.5}$