In this talk, I will survey recent developments regarding the topological classification of band-crossings in terms of crystal symmetries [1,2]. As concrete examples, I will discuss two topological materials: the Dirac nodal-line semi-metal Ca3P2 and the Weyl nodal-line semi- metal ZrIrSn.
The semi-metal Ca3P2 exhibits a line of Dirac nodes near the Fermi energy [3]. The stability of this Dirac line is guaranteed by a quantized ±π Berry phase and its low-energy physics is described by a one-parameter family of (2+1)-dimensional quantum field theories exhibiting the parity anomaly. I will show that small inversion breaking in Ca3P2 allows for an electric- field induced anomalous transverse current, whose universal component originates form the parity anomaly [4]. Due to this Hall-like current, carriers at opposite sides of the Dirac nodal ring flow to opposite surfaces when an electric field is applied. To detect the topological currents, a dumbbell device is proposed, which uses surface states to filter charges based on their momenta [4].
The nodal-line material ZrIrSn exhibits nonsymmmorphic symmetries. I will show that the presence of a mirror glide symmetry leads to the protection of two-fold degenerate Weyl lines at the Fermi energy [5], even for strong spin-orbit coupling. The monopole charges and the associated drumhead surface states of ZrIrSn and other related materials will be discussed in detail.
[1]  C.-K. Chiu, J. C.Y. Teo, A. P. Schnyder, S. Ryu, Rev. Mod. Phys 88, 035005 (2016)
[2]  Y. X. Zhao, A. P. Schnyder, Z. D. Wang, Phys. Rev. Lett. 116, 156402 (2016)
[3]  Y.-H. Chan, C.-K. Chiu, M. Y. Chou, A. P. Schnyder, Phys. Rev. B 93, 205132 (2016)
[4]  W. B. Rui, Y. X. Zhao, Andreas P. Schnyder, Phys. Rev. B 97, 161113(R) (2018)
[5]  J. Zhang, Y.-H. Chan, C.-K. Chiu, M. G. Vergniory, L. M. Schoop, A. P. Schnyder, Phys. Rev. Materials 2, 074201 (2018)