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.
@article{arxiv.1707.04576,
title = {A Class of topological nodal rings and its realization in carbon networks},
author = {Yan Gao and Yuanping Chen and Yuee Xie and Po-Yao Chang and Marvin L. Cohen and Shengbai Zhang},
journal= {arXiv preprint arXiv:1707.04576},
year = {2018}
}