Dario Bercioux (Donostia International Physics Center)
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” . I will briefy mention how these exotic solitonic solutions appear in the polyacetylene chain within the so-called SSH model . 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 . I will present our results in the context of the analogue electron simulator  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 .
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