Electronic topological transitions in high-pressure bcc metals

In 1960 Lifshitz$^{\dagger}$ pointed out that variations in the topology of the Fermi surface as a function of deformation could lead to so-called electronic topological transitions (ETT). We have carried out first-principles electronic structure calculations for the shear elastic constants of bcc vanadium, niobium, and tantalum as a function of pressure and find evidence of an ETT in each case. The transition is manifested in the form of a pronounced softening in the shear elastic constants over a particular pressure range that in turn coincides with a pressure-induced topological change in the Fermi surface. Specifically, the 3-fold degenerate $\Gamma_{25}^{\prime}$ pure $d$-state is unoccupied at low pressures but shifts to lower energy and passes through the Fermi energy as pressure is increased. We have explored the detailed nature of these transitions and suggest that they should appear rather generally in most metals. \\ \\ $^{\dagger}$ I. M. Lifshitz, Sov. Phys. JETP {\bf 11}, 1130 (1960).