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

Abstract

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.