Fig. 3: Three-dimensional band structure in correlated and non-correlated states.

Flat bands of the partially relaxed (PR) model in the a non-correlated state, and b the C₂T symmetry breaking state. The non-correlated state has Dirac points protected by C₂T symmetry at the K and K′ points as required by the C₃ symmetry. When the C₂T symmetry is broken, a gap is open at the Dirac points while, in the particular state under study, the region around Γ is weakly affected. c–f Zoom of the flat band structure for the PR model and different values of \({\eta }_{{{\rm{C}}}_{3}}\). In c, \({\eta }_{{{\rm{C}}}_{3}}=0\) and the Dirac points are placed at K and K′. If \({\eta }_{{{\rm{C}}}_{3}}\) is small, as in d, the Dirac points move in momentum but stay at μ_CNP. When its magnitude increases, as in e, f, the bands at small energies are modified displacing the Dirac points away from the chemical potential of the undoped system and creating small Fermi pockets at CNP. Hence, nematicity produces a Lifshitz transition turning a semimetal into a metal. g, h Same as c, e for the FR model in the nematic state β. In all the panels a plane is plotted at μ_CNP for reference.