Siu, Z.BChang, J.-YTan, S.GJalil, M.B.AChang, C.-RELECTRICAL AND COMPUTER ENGINEERING2020-10-202020-10-202018Siu, Z.B, Chang, J.-Y, Tan, S.G, Jalil, M.B.A, Chang, C.-R (2018). Curvature induced quantum phase transitions in an electron-hole system. Scientific Reports 8 (1) : 16497. ScholarBank@NUS Repository. https://doi.org/10.1038/s41598-018-34903-920452322https://scholarbank.nus.edu.sg/handle/10635/177806In this work, we study the effect of introducing a periodic curvature on nanostructures, and demonstrate that the curvature can lead to a transition from a topologically trivial state to a non-trivial state. We first present the Hamiltonian for an arbitrarily curved nanostructure, and introduce a numerical scheme for calculating the bandstructure of a periodically curved nanostructure. Using this scheme, we calculate the bandstructure for a sinusoidally curved two-dimensional electron gas. We show that the curvature can lead to a partner switching reminiscent of a topological phase transition at the time reversal invariant momenta. We then study the Bernevig-Hughes-Zhang (BHZ) Hamiltonian for a two-dimensional quantum well. We show that introducing a curvature can lead to the emergence of topological surface states. © 2018, The Author(s).Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Article