Winding Vector: How to Annihilate Two Dirac Points with the Same Charge


G. Montambaux, Lim, L. - K., Fuchs, J. - N., and Piechon, F., “Winding Vector: How to Annihilate Two Dirac Points with the Same Charge”, PHYSICAL REVIEW LETTERS, vol. 121, p. 256402, 2018.


The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite (+- scenario) or identical (++ cenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the same winding number emerge under appropriate distortion (interaction, etc.), following the ++ scenario. Under further distortion, these Dirac points merge following the +- scenario, that is corresponding to opposite winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.