Experimental design and theoretical model building for higher-order topological insulators*

Higher-order topological states establish a new complexity class of topological matter. The contemporary challenge is to devise experimental scenarios in which such exotic states of matter can unfold. We report on a synthetic topological matter realization of a quadrupolar topological insulator in a topolectrical circuit array [Imhof et al., Nature Physics 14, 925 (2018)]. Transcending from specific realizations of this phenomenon, we attempt to draw a line to previous observations of dimensional edge mode hierarchies [Sessi et al., Science 354, 1269 (2016)] before the field's terminology first emerged in 2017.