“…For an n th-order topological insulator (TI) in d spatial dimensions, protected in-gap states are featured at its d – n dimensional boundary with 1 < n ≤ d . Among various HOTIs, two-dimensional (2D) second-order topological insulators (SOTIs) that possess a gapped bulk and no gapless edge states have attracted enormous research interest. − A 2D SOTI manifests topologically protected 0-dimensional (0D) corner states, which are usually depicted by fractionally quantized corner charge whose quantization is symmetry protected and can change in discrete jumps at topological phase transitions. − Currently, although the 2D SOTI phase has been proposed for a long time, almost all of the experimental observations have only been verified in artificial crystal systems, such as photonic systems, − acoustic systems, − and electric circuits. − Despite being the most crucial frontier of topological matter, 2D SOTI phases in electronic materials have not yet been found in experiments, posing a great obstacle for further studies on higher-order topological physics and related application research.…”