  We report on the investigation of plasmonic resonances in metallic M\"obius
nanorings. Half-integer numbers of resonant modes are observed due to the
presence of an extra phase {\pi} provided by the topology of the M\"obius
nanostrip. Anomalous plasmon modes located at the non-orientable surface of the
M\"obius nanoring break the symmetry that exist in conventional ring cavities,
thus enable far-field excitation and emission as bright modes. The far-field
resonant wavelength as well as the feature of half-integer mode numbers is
invariant to the change of charge distribution on the M\"obius nanoring due to
the nontrivial topology. Owing to the ultra-small mode volume induced by the
remaining dark feature, an extremely high sensitivity as well as a remarkable
figure of merit is obtained in sensing performance. The topological metallic
nanostructure provides a novel platform for the investigation of localized
surface plasmon modes exhibiting unique phenomena in plasmonic applications
such as high sensitive detection and plasmonic nanolasers.
