First-Principles Study On The Phase Transition Of The Charge Density Wave Of Transition Metal Dichalcogenides

One of the most notable materials in condensed matter physics is transition metal dichalcogenides（TMDs）,the research of which is now developing rapidly in many di-rections such as valleytronics,Berry phase-related physics,and topological properties.It is well known that the charge density wave（CDW）induced by the Peierls transition often only occurs in one-dimensional systems.Recently,rich charge density wave（CDW）phases have been discovered in 2D TMDs,which are closely related to the magnetic,superconducting,and topological properties of TMDs,thus reviving strong interest in CDWs.CDWs in 2D TMDs are now are becoming is a frontier topic that has received wide attention in the experimental and theoretical condensed matter physics.However,the current research is not perfect,many experimental results need to be ex-plained,there are inconsistencies in different experimental observations of the same material,and different theoretical models give different predictions of the CDWs.In view of this,it is necessary to conduct more in-depth studies on CDW in TMDs.In this dissertation,we study the CDW phase transition in TMD based on the first-principles method.It is found that temperature,thickness,charge doping and magnetic field can effectively modulate the CDW phase.A series of new CDW phases have been discov-ered and a theoretical explanation is given for the inconsistenies in the experiments.The major findings are as follows:1.The CDW phase transitions in NbS₂.The current research on the CDW phase in NbS2 has encountered difficulties.There are inconsistent experimental results:no evi-dence of CDW phase was found in NbS₂/Au,while another experiment reported the existence of 3×3 CDW phase in NbS₂/graphene.Previous calculations predicted a pos-sible CDW phase transition in monolayer NbS₂,but did not determine the atomic and electronic structure of the CDW phase.Studies have suggested that the CDW of NbS₂is sensitive to external conditions,but how it depends on temperature,thickness,and charge doping remains unknown.We find by first-principles calculations that a 2×2CDW phase exists within harmonic approximation at higher temperatures for mono-layer NbS₂.At low temperature,it transforms into the 3×3 CDW phase.We determined its atomic structure and the corresponding STM image,which is consistent with the experiments.Since the CDW phase transition breaks the symmetry,the band gap near the high symmetry point K is opened,and the charge distribution becomes highly asym-metric,making the thermal,mechanical,and electronic properties of NbS₂ get after the CDW phase transition highly anisotropic.We explored the modulation of the CDW phase by electron doping in monolayer NbS₂ and found that slight electron doping could eliminate the 3×3 CDW phase,while increasing the doping level would in turn lead to new 2×2 and 4√3×4√3 CDW phases.Furthermore,the charge analysis of NbS₂/Au and NbS₂/graphene showed that Au doped NbS₂ with significantly more elec-trons compared with graphene,thus clarifying why 3×3 CDW was observed only in graphene-supported NbS₂ phase,but not found in NbS₂/Au.It is found that the CDW is stable with relatively small strain perturbations.By calculating and comparing the projected phonon density of states of NbS₂,NbSe₂ and Janus-SNbSe,the reason why NbS₂ and NbSe₂ appear to be highly similar while their CDW phases are very different is explained.We further investigated the dependence of the relative thickness of CDWs in few-layer NbS₂.In bilayer NbS₂,it was found that the low temperature 3×3 CDW remains.At lower temperatures,the calculations found a new 4×4 CDW phase.While in triple-layer NbS₂,the 3×3 CDW phase is suppressed and no other CDW phases ap-pear,indicating that the 3×3 CDW phase disappears with increasing thickness,which is consistent with the experiments.2.The CDW phase of Janus-SeNbS and comparative study of NbS₂ and NbSe₂ CDW phases.NbS₂ and NbSe₂ appear to be highly similar,but experimental and theoretical studies have found that their CDW properties are significantly different.The 3×3 CDW phase of NbSe₂ is easily observed,and has both triangule and star configurations.The3×3 CDW phase of NbS₂ is difficult to observe and has only one configuration.The cause of this problem remains to be discovered.To this end,we calculated the projected phonon density of states of NbS₂ and NbSe₂,and found that the phonon density of states of Se is much larger than that of S in the imaginary frequency range,indicating that Se atoms are more active in vibration than S atoms,and hence the displacement of Se atoms is larger.We also study the CDW phase of Janus-SeNbS and calculate its pro-jected phonon density of states,which directly confirms that the vibration of Se atoms is far more active than that of S atoms.Therefore,it can be explained that NbSe₂ is more prone to CDW phase transition and more likely to form different CDW configu-rations.At the same time,we also calculated the phonon dispersion of Janus-SeNbS and obtained the atomic structure of its 3×3 CDW phase,which was found to be similar to the triangule configuration of NbSe₂ and NbS₂.3.CDW phase transition study in 1T-VSe₂ material.1T-VSe₂ is a magnetic material and a typical CDW wave material with multiple CDW phases.Its magnetic configura-tion and CDW phases have a competitive relationship.We performed a series of theo-retical calculations on the phonon spectrum of monolayer 1T-VSe₂ using first-princi-ples methods.By changing the broadening parameters to simulate temperature modu-lation,it is found that the imaginary frequency existing betweenΓand K points corre-sponds to the experimentally found√7×√3 CDW phase when the temperature is higher.The atomic structure of the√7×√3 phase is obtained by relaxation along the vibrational mode direction of this imaginary frequency,and its electronic properties are also calculated.When considering the magnetism of the monolayer 1T-VSe₂,the imag-inary frequency of the phonon spectrum completely disappears,indicating that the CDW phase disappears at this time.On this basis,we consider the effect of strain.It is found that with the increase of tensile strain,the magnetic moment increases,and the imaginary frequency of the CDW phase reappears.As the compressive strain increases,the magnetic moment decreases.When the compressive strain is very small,the imag-inary frequency of the CDW phase appears.As the compressive strain continues to in-crease,and the imaginary frequency disappears,indicative of the vanishing of the CDW phase.