Theoretical study of CDW phases for bulk NbX₂ (X = S and Se)

In most two-dimensional transition metal chalcogenides, the superconducting phase coexists with the charge density wave (CDW) phase. There exists at least one case, i.e. bulk 2H-NbS₂, that does not conform to this picture. Scientists have shown great interest in trying to experimentally find the CDW phase of bulk NbS₂ since 1975. Is there any theoretically more stable thermodynamic state than its higher-temperature metal phase, especially in the case of charge injection? Theoretically more stable CDW bulk configurations (TC for 2H-NbS₂ and TTs for 2H-NbSe₂) with partial pseudo energy gaps were predicted through the harmonic phonon softening theory and first-principles calculations. The ratios of larger to smaller pseudo gaps around K-H segment in the Brillouin zone for CDW phases are basically equal to those of superconductivity phases for bulk 2H-NbX₂ (X = S and Se). The CDW phase should coexist with its superconductor state below the critical temperature rather than the metal phase for bulk 2H-NbS₂. The presence of CDW phase should be more easily observed experimentally when the injected charge reaches 0.5e/Nb₁₈S₃₆ for bulk 2H-NbS₂. Our calculations of density of state (DOS) indicated that, during Nb atoms contracting to form the CDW phases with symmetry breaking in the in-plane direction, dominant conductive carriers are always of p-type for bulk 2H-NbS₂ while the alternation of carrier type from p-type to n-type occurs for bulk 2H-NbSe₂. The Fermi level continuously drops and then the M-L segment of the out-of-plane energy band emerges from the Fermi surface, which corresponds to the reversal of p-n type sign. Lifshitz transition of pocket-vanishing types occurs in the out-of-plane direction without symmetry breaking during the geometrical structural phase transition for bulk 2H-NbSe₂. Our calculations have theoretically addressed the long-standing coexistence issue of CDW and superconducting phases.