Quadrupole topological insulators in Ta$_2M_3$Te$_5$ ($M=$ Ni, Pd) monolayers

Abstract

Higher-order topological insulators have been introduced in the precursory BBH quadrupole model, but no electronic compound has been proposed to be a quadrupole topological insulator (QTI) yet. In this work, we predict that Ta2M3Te5 (M = Pd, Ni) monolayers can be 2D QTIs with second-order topology due to the double-band inversion. A time-reversal-invariant system with two mirror reflections (Mx and My) can is classified by Stiefel-Whitney (SW) numbers (w1, w2) due to the combined symmetry T C2z. Using the Wilson loop method, we compute w1 = 0 and w2 = 1 for Ta2Ni3Te5, indicating a QTI with q xy = e/2. Thus, gapped edge states and localized corner states are obtained. By analyzing atomic band representations, we demonstrate that its unconventional nature with an essential BR at an empty site, i.e., Ag@4e, is due to the remarkable double-band inversion on Γ-Y. Then, we construct an eight-band quadrupole model with Mx and My successfully for electronic materials. These transition-metal compounds of A2M1,3X5 family provide a good platform for realizing the QTI and exploring the interplay between topological order and interactions.