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Lifshitz transition was proposed to explain a change of the topology structure in a Fermi surface induced by continuous lattice deformation without symmetry breaking since 1960. It is well known that the anomalies of the kinetic coefficients (the coefficient of heat conduction and electrical conductivity, viscosity, sound absorption, etc.) are usually closely connected with the Lifshitz transition behavior. 2H-TaS2 is a typical representative to study its anomalies of temperature dependence of heat capacity, resistivity, Hall effect, and magnetic susceptibility. Its geometrical structure of the charge density wave (CDW) phase and layer number dependence of carrier-sign alternation upon cooling in the Hall measurements have not been well understood. The geometrical structure (T–Ts) of the CDW phase was predicted through first principles calculations for bulk and mono-layer 2H-TaS2. Driven by electron-lattice coupling, Ta atoms contract to form a partially gapped CDW phase. The CDW phase has a larger average interlayer separation of S–S atoms in the adjacent two layers compared with the metal phase, which results in a weaker chemical bonding among S–S atoms in the adjacent two layers and then a narrower bandwidth of the energy band. The narrower bandwidth of the energy band leads to a larger density of states (DOS) in the out-of-plane direction above the Fermi level for the CDW phase. As the Fermi level continually drops from the DOS region with a negative slope to that with a positive slope on cooling, the reversal of the p → n type carrier and the pocket-vanishing-type Lifshitz transition occur in the bulk 2H-TaS2. However, the Fermi level slightly drops by 6 meV and happens to be at the positions of pseudo band gaps, so the reduction of in-plane DOS and total DOS is responsible for the always p-type carrier in the mono-layer samples. Our CDW vector of the k-space separation between two saddle points is QSP ≈ 0.62 GK and can provide a theoretical support for the "saddle-point" CDW mechanism proposed by Rice and Scott. Our theoretical explanation gives a new understanding of both Lifshitz transition for symmetry breaking and reversal for the p–n carrier sign in the Hall measurements in various two-dimensional transition metal disulfides. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Aiming at the frequency synchronization phenomena of oscillating or rotating bodies, this paper proposes a novel solution to address the self-synchronization problem of vibration systems. An integral mean method with small parameters and periodic coefficient (IMM-SPPC) is proposed, which converts the relative motion of the electrically driven eccentric rotor and the vibration environment into a second-order periodic coefficient differential equation. Through the calculation of the equilibrium point of the second-order periodic coefficient differential equation and the study of its stability, the synchronization criterion and the stability criterion of the eccentric rotor and the vibration environment are deduced. The simulation results show the validity of the deduced synchronization criterion and stability criterion. The proposed IMM-SPPC provides a new way for studying vibration synchronization.

Phase stability and the phase transition of Janus transition metal chalcogenides (TMDs) have become interesting issues that have not been fully resolved since their successful synthesis. By fitting the results from first principles calculations, a tight-binding dynamics matrix of the 1T′ phase is constructed and the eigenvectors are also obtained. We propose a method to project the atomic motion causing the phase transition from 2H to 1T′ onto these eigenvectors, and identify four key phonon modes which are the major factors to trigger phase transition. Temperature excitation is used to excite the key modes and the free energy criterion is used to determine the phase stability. The relatively large enthalpy difference between the 2H and 1T′ phases favours the 2H one as the stable phase at low temperature. While the 1T′ phase has a quick increase in vibrational free energy with rising temperature, especially for 1T′ Janus TMDs which have a quicker increase in the total free energy than that of 1T′ non-Janus TMDs, making them show a lower phase transition temperature. Our work will deepen our understanding of the phase transition behavior of 2D Janus TMDs, and the tight-binding dynamics matrix and the method to obtain the key modes will be a useful tool for further study of the phase transitions of 2D Janus TMDs and other related materials. [ABSTRACT FROM AUTHOR]