Topological materials and topological responses

The past decade has witnessed intensive research aimed at investigating the role of band-structure topology and discovering topological materials. The topology provides a new aspect to understand the band-structure and reveal exotic phenomena, such as topological surface states. In this talk, I will focus on recently-discovered Weyl semimetals. Besides the unique Fermi arc surface states, I will introduce the transport and optical phenomena in realistic materials, which include the linear response (e.g. anomalous Hall and spin Hall effects) and nonlinear response (second-harmonic generation and dc photocurrents) induced by the Weyl band structure.

Refs. Annu. Rev. Condens. Matter Phys. 8, 337-354 (2017); Nature Physics 11, 728 (2015); arXiv:1708.08589, and arXiv:1803.00562.