Square-root higher-order topological insulators and topological semimetals

Recently, square-root topological insulators, whose topological properties are inherited from the squared Hamiltonian, have attracted interests from both theoretical and experimental points of view. Most of the examples proposed or realized so far are 1D, first-order topological insulators.
In this presentation, we address several extensions of the square-root topological insulator, taking a 2D decorated honeycomb model as an example. The square of the model becomes the direct sum of the honeycomb and kagome models. In this model, we propose (i) the square-root higher-order topological insulator [1], where finite-energy corner modes emerge, and (ii) the square-root topological semimetal [2], where finite-energy Dirac cones emerge. We elucidate the topological aspects of the decorated honeycomb model inherited from the squared Hamiltonian, and the characteristic bulk-boundary correspondence. If time allows, we also address generalization of the model construction scheme and possible realization in artificial materials.

[1] TM, Y. Kuno, and Y. Hatsugai, PRA 102, 033527 (2020)
[2] TM, T. Yoshida, and Y. Hatsugai, arXiv:2008.12590