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Negative Refraction Induced by Möbius Topology

We theoretically show the negative refraction existing in Möbius molecules. The negative refractive index is induced by the non-trivial topology of the molecules. With the Möbius boundary condition, the effective electromagnetic fields felt by the electron in a Möbius ring is spatially inhomogeneous. In this regard, the $D_{N}$ symmetry is broken in Möbius molecules and thus the magnetic response is induced through the effective magnetic field. Our findings open up a new architecture for negative refractive index materials based on the non-trivial topology of Möbius molecules.