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Recent experiments showed the distinct observations on the transition metalditelluride NiTe$_2$ under pressure: one reported a superconducting phasetransition at 12 GPa, whereas another observed a sign reversal of Hallresistivity at 16 GPa without the appearance of superconductivity. To clarifythe controversial experimental phenomena, we have carried out first-principleselectronic structure calculations on the compressed NiTe$_2$ with structuresearching and optimization. Our calculations show that the pressure cantransform NiTe$_2$ from a layered P-3m1 phase to a cubic Pa-3 phase at $\sim$10GPa. Meanwhile, both the P-3m1 and Pa-3 phases possess nontrivial topologicalproperties. The calculated superconducting $T_c$'s for these two phases basedon the electron-phonon coupling theory both approach 0 K. Further magnetictransport calculations reveal that the sign of Hall resistance for the Pa-3phase is sensitive to the pressure and the charge doping, in contrast to thecase of the P-3m1 phase. Our theoretical predictions on the compressed NiTe$_2$wait for careful experimental examinations.

First-principles study of the crystal structure, electronic structure, and transport properties of NiTe$_2$ under pressure