Topological Effects in 1D and 2D Materials: Topological Band Engineering, Optical Selection Rules, and Excitonic Shift Currents*

In this talk, I present several fascinating manifestations of topological effects in the electronic and optical properties of atomically thin one-dimensional (1D) and two-dimensional (2D) materials. First, we find that symmetry-protected topological phases exist in graphene nanoribbons (GNRs) [1]. Semiconducting GNRs of different width, edge shape, and terminating unit cells can belong to different electronic topological classes, characterized by a Z₂ invariant. Junctions between segments of topologically distinct GNRs are predicted to support robust in-gap topological junction states which can be used for band engineering. Experimental realizations of these predictions have been achieved [2]. Second, we show that the conventional optical selection rules for excitons must be replaced in 2D by a novel simpler formula, owing to a topological characteristic inherent to the photoexcitation of excitons in 2D [3]. The new selection rule is dictated by a winding number of the interband optical transition matrix elements (a heretofore unrecognized topological invariant). This appealingly simple and general new rule is applied to elucidate the optical spectra of gapped graphene systems. Third, I present some recent work on the effects of electron-hole interactions on shift currents in non-centrosymmetric 2D crystals (so-called bulk photovoltaic effect), in which we show excitonic effects lead to an enormous enhancement and, more interestingly, gives rise to DC conduction with sub-bandgap-frequency excitations.[4]
References:
[1] T. Cao, F.-Z. Zhao, and S. G. Louie, Phys. Rev. Lett. 119, 076401 (2017)
[2] D. J. Rizzo, et al., Nature 560, 204 (2018)
[3] T. Cao, M. Wu, and S. G. Louie, Phys. Rev. Lett. 120, 087402 (2018)
[4] Y.-H. Chan, D. Y. Qiu, F. H. da Jornada, and S. G. Louie, submitted.