Common wisdom has it that edge states appear only in topological systems, e.g., topological insulators and topological superconductors. In this talk I will discuss edge states in topological and non-topological InAsBi quantum dots described by a confined Bernevig-Hughes-Zhang model. Interestingly we find that these quantum dots exhibit protected helical edges states both in the topological and non-topological regimes [1]. I will also briefly discuss edge states in Chern insulators and nodal semimetals which display trivial edge states not arising from band topology (Chern number) [2]. In this case the approximate chiral symmetry of the Chern insulator (exact only in the nodal semimetal) is the relevant ingredient behind the appearance of these trivial edge states. This work was supported by CNPq, CAPES, UFRN/MEC, FAPESP, PRP-USP/Q-NANO, German Science Foundation (DFG) via Grant No. SFB 1170 “ToCoTronics” and the ENB Graduate School on Topological Insulators and the Center for Emergent Materials, and NSF MRSEC under Award No. DMR-1420451.

[1] D. R. Candido, M. E. Flatté and J. C. Egues, accepted in Phys. Rev. Lett., arXiv:1803.02936.
[2] D. R. Candido, M. Kharitonov, J. C. Egues, and E. Hankiewicz, Phys. Rev. B 98, 161111(R) (2018).