A class of topological nodal rings and its realization in carbon networks

Abstract

Topological nodal rings can be classified into three types according to the slopes in their energy dispersion. Type-I nodal rings consist of type-I points, type-II rings consist of type-II points, and type-III rings consist of anisotropic points. Taking carbon networks as an example, we show that all three types can exist and transform from one to another under experimentally realizable strain. Within a given type, a transition between a topological metal phase and a semiconductor phase also takes place, and each type of nodal rings shrinks into the corresponding type of semi-Dirac points, including novel type-II and -III semi-Dirac points. These topological features are expected to exhibit diverse electron-hole pocket patterns and Landau levels, giving rise to unusual transport properties.