Where are we in the jungle of topological materials?

It is just about a decade ago that the quantum-spin-Hall insulator state was observed in HgTe/CdTe quantum wells, followed by the realization of the 3D topological insulator state in BiSb alloys. These discoveries launched an intense worldwide effort on topological states protected by time-reversal symmetry constraints and the associated exotic phenomena, leading to the Nobel Prize in physics in 2016. Last few years have seen a great expansion of the field, which now encompasses protected states of quantum matter that arise through combinations of time-reversal, crystalline and particle-hole symmetries. Despite these advances, the field is still in its infancy and many more surprises can be expected involving 2D and 3D topological materials and their interfaces and heterostructures with magnetic, non-magnetic and superconducting materials. I will highlight some of the progress that has been made, including our own recent work [1-6], and comment on the outstanding open questions.

[1] Bansil, Lin and Das, Reviews of Modern Physics 88, 021004 (2016).
[2] Xu et al., Science Advances 3, e1603266 (2017).
[3] Vargas et al., Science Advances 3, e1601741 (2017).
[4] Chang et al., Physical Review Letters 119,156401 (2017).
[5] Okada et al., Physical Review Letters 119, 086801 (2017).
[6] Chang et al., Physical Review Letters (2017).