  Topological nodal rings can be classified into three types according to the
slopes in their energy dispersion. The first two are made of type-I and II
nodal points, respectively, while the third is made of both. In carbon
networks, all three types can exist. Under strain, phase transitions from a
topological metal to a semiconductor, take place, and at the transition points,
these nodal rings shrink into type-I, II, and III semi-Dirac points. These
topological features exhibit diverse electron-hole pocket patterns and Landau
levels, which give rise to exotic transport properties.
