Topolectrical circuit simulation of two-dimensional graphyne structures

Graphyne and its family members are two-dimensional (2D) carbon allotropes with both $sp$ and $s{p}^{2}$ hybridizations. Authors of recent investigations have highlighted the potential of graphyne as a promising material for exploring both higher-order topological insulators (HOTIs) and semimetals. In this paper, we report the experimental observation of the corner states in 2D graphyne circuit network, which are protected by spatiotemporal inversion symmetry and characterized by the bulk polarization. Furthermore, we demonstrate that an intriguing Weyl semimetal phase emerges during the transition from topological insulating phase to trivial phases, where the Weyl point moves along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}M$ line before the band gap reopens. In this paper, we provide both theoretical and experimental evidence to underpin the graphyne structure for realizing both HOTIs and semimetals.