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The merging or emergence of a pair of Dirac points may be classifiedaccording to whether the winding numbers which characterize them are opposite($+-$ scenario) or identical ($++$ scenario). From the touching point betweentwo parabolic bands (one of them can be flat), two Dirac points with the {\itsame} winding number emerge under appropriate distortion (interaction, etc),following the $++$ scenario. Under further distortion, these Dirac points mergefollowing the $+-$ scenario, that is corresponding to {\it opposite} windingnumbers. This apparent contradiction is solved by the fact that the windingnumber is actually defined around a unit vector on the Bloch sphere and thatthis vector rotates during the motion of the Dirac points. This is shown herewithin the simplest two-band lattice model (Mielke) exhibiting a flat band. Weargue on several examples that the evolution between the two scenarios isgeneral.

Winding vector: how to annihilate two Dirac points with the same charge