2018/04/03 by Gilles Montambaux, Lih-King Lim, Jean-Noël Fuchs +1 · 1 citation
Physics and Astronomy · #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.121.256402
published as Phys. Rev. Lett. 121, 256402 (2018) · 5 pages, 6 figures
arxiv created 2018/04/03 · arxiv updated 2018/12/21
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 (++ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the \it 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 \it 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.