Edge Majoranas on locally flat surfaces - the cone and the M\"obius band

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For any physical system the Hamiltonian would also have terms which does not depend on the intrinsic geometry, but for simplicity we do not consider such terms here

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For the interaction to be well defined, the Fourier transform V ⁡ ( q ) V(q) of the potential V ⁡ ( r ) V(r) , where r r is the geodesic distance, have to vanish as q → ∞ q\rightarrow\infty . However, the precise behaviour at large momenta is not important for the long wave-length physics

Cited in the paper.

Adding higher-order terms would also mean that the ansatz Δ ​ ϕ = c ​ o ​ n ​ s ​ t . \Delta\phi=const. is not a self-consistent solution close to vortices or edges

Cited in the paper.

There are many such flat embeddings, and it is interesting to ask which one would minimize the elastic energy for a real physical Möbius band. This problem was recently solved numerically in Ref. \rev@citealpnum

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