Negative Refraction Induced by M\"obius Topology

We theoretically show the negative refraction existing in M\"{o}bius molecules. The negative refractive index is induced by the non-trivial topology of the molecules. With the M\"{o}bius boundary condition, the effective electromagnetic fields felt by the electron in a M\"{o}bius ring is spatially inhomogeneous. In this regard, the $D_{N}$ symmetry is broken in M\"{o}bius 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 M\"{o}bius molecules.