Origin of the critical temperature discontinuity in superconducting sulfur under high pressure

Elemental sulfur shows a superconducting phase at high pressure (above 100 GPa), with critical temperatures that rise up to 20 K [Phys. Rev. B 65, 064504 (2002); Nature (London) 525, 73 (2015)] and presenting a jump at about 160 GPa, close to a structural phase transition to the $\ensuremath{\beta}$-Po phase. In this work we present a theoretical and fully ab initio characterization of sulfur based on superconducting density functional theory (SCDFT), focusing in the pressure range from 100 to 200 GPa. Calculations result in very good agreement with available experiments and point out that the origin of the critical temperature discontinuity is not related to the structural phase transition but induced by an electronic Lifshitz transition. This brings a strongly (interband) coupled electron pocket available for the superconducting condensation.