Origins of low- and high-pressure discontinuities of $T_{c}$ in niobium
  The discontinuities of $T_{c}$ in Niobium under pressure are examined by means of the pseudopotential plane-wave implementation of the electron-phonon coupling calculated from density-functional perturbation theory. Both low- and high-pressure discontinuities of $T_{c}$ have their origin in the Kohn anomalies and are caused by the low-frequency phonons, but the mechanism leading to the discontinuities is different in the two cases. The low-pressure anomaly is associated with a global decrease of the nesting factor in the whole Brillouin Zone and not to a visible change in the band structure. The high-pressure anomaly is instead connected with a well-pronounced change in the band structure. 
Malgorzata Wierzbowska, Stefano de Gironcoli, Paolo Giannozzi