I'm refering to the Paper: PHYSICAL REVIEW B 80, 195310 (2009) "Möbius graphene strip as a topological insulator" Z. L. Guo, Z. R. Gong, H. Dong, and C. P. Sun.
The paper is also available as a preprint version via: http://arxiv.org/abs/0906.1634
When I'm refering to an equation, I'll also use the arxiv-reference (since it's freely available).
I'm refering to Section II: Edge States in Möbius Graphene Strip, Equations (12), (13).
I can show that these linear combinations do indeed satisfy the periodic boundary conditions. What I do not see is why you have to use y>0 and y<0 in the proof? At which stage of the periodicity proof does one need to distinguish between y>0 and y<0?
It's true that is seems to be a natural distinction, because one can cut the moebius strip in the middle and obtain two cylinders as shown in Fig 3.
I'd be more than happy on some advice.