The role of the phonon anomaly in the superconductivity of vanadium and selenium under high pressures

First-principles calculations were performed for the superconductivity of vanadium and selenium under high pressures. The superconducting transition temperature T-c of bcc vanadium, obtained as a function of pressure, shows a considerable increase, at first linearly, with pressure, and then the rate of increase of T-c is abated around 80 GPa. The calculated pressure dependence of T-c shows qualitatively the same behaviour as the experimental result. This characteristic behaviour of T-c as a function of pressure is attributed to a remarkable phonon anomaly, i.e. frequency softening of the transverse mode around a quarter of the Gamma-H line with increasing pressure. The superconducting transition temperature T-c, calculated for two high-pressure phases of solid selenium, bcc and beta-Po, also shows a characteristic pressure dependence. In bcc Se, Tc increases considerably with decreasing pressure and its maximum exceeds 10 K. In beta-Po Se, T-c is less pressure dependent and much lower than that of bcc Se. There is a large jump in T-c at the transition pressure from bcc to beta-Po with decreasing pressure. The remarkable increase of T-c with decreasing pressure in bcc Se is attributed also to a phonon anomaly, i.e. a frequency softening of the transverse mode in the middle of the Gamma-N line with decreasing pressure.