Analogous quadrupole topology induced by non-Hermiticity

Abstract

Non-Hermiticity can alter the topological phases of Hermitian lattices and induce gapped edge states and in-gap corner states for the topologically trivial structures in Hermitian cases. To date, however, the realizations of non-Hermiticity-induced higher-order topological phases have often needed intricate designs, where the non-Hermitian systems on a square lattice are comprised of 16 atoms per unit cell with staggered on-site non-Hermitian components at least. It is still necessary to further investigate their topological characteristics in both Hermitian and non-Hermitian systems. In this paper, we suggest an extended quadrupole topological insulator that contains eight atoms in each unit cell and whose topological phases in Hermitian cases are governed by the couplings between adjacent atoms. By introducing external losses into such a higher-order topological insulator, we show that therein the trivial lattices can also give rise to nontrivial quadrupole topology with higher-order corner states. Calculating the biorthogonal nested Wilson loop characterizes the topology for such a non-Hermitian system. Interestingly, the non-Hermitian system has four Wannier bands, with two near zero and two deviating from zero and distributing symmetrically in the negative and positive sections, implying a topology similar to the nontrivial phase in the Hermitian case. Furthermore, both the positive and negative Wannier bands exhibit a nontrivial polarization of 0.5 whereas the remain Wannier bands near zero carry a trivial polarization, indicating that the non-Hermitian system hosts a nontrivial quadrupole topology. We also propose a complete design with acoustic resonators to implement the homologous non-Hermitian topology in acoustic systems to validate our theory. The numerical results match the analytical solution perfectly. Our work introduces an alternative method for fabricating non-Hermitian-induced quadrupole topological insulators and paves the way for future research into the non-Hermitian higher-order topology.