Title: High-order topological states in electronic and photonic lattice systems

Abstract: In this seminar, I will talk about crystalline topological electronic and photonic lattice systems. For pedagogical reasons, I will start with Jackie and Rabbi’s milestone work on “Solitons with fermion number 1/2” [1]. I will briefy mention how these exotic solitonic solutions appear in the polyacetylene chain within the so-called SSH model [2]. In this contest, I will show how the study of these systems evolved from one-dimensional to higher-dimensions, giving rise to the concept of high-order topological insulators [3]. I will present our results in the context of the analogue electron simulator [4] and photonic crystals [5-8]. I will review the various known topological phases in the condensed matter framework, including the newly postulated fragile topological phase [9].

References
[1] Jackiew & Rebbi, Phys. Rev. D 133, 3398 (1976).
[2] Su, Schriffer & Heeger, Phys. Rev. Lett. 42, 1698 (1979); Phys. Rev. B 22, 2099 (1080).
[3] Benalcazar, Bernevig & Hughes, Science 357, 61 (2017). [4] Kempkes et al., Nat. Mates. Nat. Mater. 18, 1292 (2019).
[5] M. B. de Paz et al., Phys. Rev. Research 1, 032005 (2019).
[6] M. B. de Paz et al., Adv. Quantum Technol. 3, 1900117 (2020).
[7] M. Proctor et al., Phys. Rev. Research 2, 042038 (2020).
[8] M. Proctor et al., Appl. Phys. Lett. 118, 091105 (2021).
[9] H. C. Po, H. Watanabe, & A. Vishwanath, Phys. Rev. Lett. 121, 126402 (2018).

Talk – Video

Talk – Slides