Quadrupole topological insulators in Ta2M3Te5 (M= Ni, Pd) monolayers

Higher-order topological insulators have been introduced in the precursory Benalcazar-Bernevig-Hughes quadrupole model, but no electronic compound has been proposed to be a quadrupole topological insulator (QTI) yet. In this work, we predict that Ta$_2M_3$Te$_5$ ($M=$ 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 (M$_x$ and M$_y$) can be classified by Stiefel-Whitney numbers ($w_1, w_2$) due to the combined symmetry $TC_{2z}$. Using the Wilson loop method, we compute $w_1=0$ and $w_2=1$ for Ta$_2$Ni$_3$Te$_5$, 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 band representation at an empty site, i.e., $A_g@4e$, is due to the remarkable double-band inversion on Y-$\Gamma$. Then, we construct an eight-band quadrupole model with $M_x$ and $M_y$ successfully for electronic materials. These transition-metal compounds of $A_2M_{1,3}X_5$ ($A$ = Ta, Nb; $M$ = Pd, Ni; $X$ = Se, Te) family provide a good platform for realizing the QTI and exploring the interplay between topology and interactions.