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Linear crossing of energy bands occur in a wide variety of materials. In thispaper we address the question of the quantization of the Berry windingcharacterizing the topology of these crossings in dimension $D=2$. Based on thehistorical example of $2$-bands crossing occuring in graphene, we propose torelate these Berry windings to the topological Chern number of a $D=3$dimensional extension of these crossings. This dimensional embedding isobtained through a choice of a gap-opening potential. We show that the presenceof an (emergent) $\mathcal{PT}$ symmetry, local in momentum and antiunitary,allows us to relate $D=3$ Chern numbers to $D=2$ Berry windings quantized asmultiple of $\pi$. We illustrate this quantization mechanism on a variety ofthree-band crossings.

Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry