Physikalische Chemie - Direktor: Prof. Dr. Martin Wolf

Department Seminar

Host: R. Ernstorfer

Monday, February 4, 2019, 11:00 am

PC Seminar Room, G 2.06, Faradayweg 4

Dr. Andreas Schnyder

Quantum Many Body Theory Department, Max Planck Institute for Solid State Research, Stuttgart.

Crystalline topological semi-metals

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,

[2] Y. X. Zhao, A. P. Schnyder, Z. D. Wang,

[3] Y.-H. Chan, C.-K. Chiu, M. Y. Chou, A. P. Schnyder,

[4] W. B. Rui, Y. X. Zhao, Andreas P. Schnyder,

[5] J. Zhang, Y.-H. Chan, C.-K. Chiu, M. G. Vergniory, L. M. Schoop, A. P. Schnyder,

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)