Temperature and pressure induced electronic topological transitions in titanium

The electronic topological transitions (ETT) in d-transition metals are considered using titanium as an example. It is shown that, upon a temperature- or pressure-induced transition from the ω-phase to the α-phase, the chemical potential shifts to the region of topological features of the electronic energy spectrum, characterized by a negative curvature of the density of states of d-electrons (DOS). As a result, the sign of the mode-mode interaction parameter changes. The ETT leads to an increase in paramagnon Bose excitations and to the appearance of spatial fluctuations of electron density waves. It is shown that a sharp decrease in volume during the transition from the hp ω-to hcp α-phase is the result of the ETT. In this case, the obtained numerical values are in agreement with the experimental data at normal pressure. Entropy calculations show that paramagnons and spatial fluctuations of the electron density are of the most important reasons for the thermodynamic stability of the titanium structural phases.