Engineering a non-Hermitian second-order topological insulator state in quasicrystals

Non -Hermitian topological phases have gained immense attention due to their potential to unlock novel features beyond Hermitian bounds. PT -symmetric (parity time -reversal symmetric) non -Hermitian models have been studied extensively over the past decade. In recent years, the topological properties of general non -Hermitian models, regardless of the balance between gains and losses, have also attracted vast attention. Here, we propose a non -Hermitian second -order topological (SOT) insulator that hosts gapless corner states on a two-dimensional quasicrystalline lattice (QL). We first construct a non -Hermitian extension of the BernevigHughes-Zhang model on a QL generated by the Amman-Beenker tiling. This model has real spectra and supports helical edge states. Corner states emerge by adding a proper Wilson -mass term that gaps out the edge states. We propose two variations of the mass term that result in fascinating characteristics. In the first variation, we obtain a purely real spectra for the second -order topological phase. In the latter, we get a complex spectra with corner states localized at only two corners due to the higher -order non -Hermitian skin effect of the edge modes. Our findings pave a path to engineering exotic SOT phases where corner states can be localized at designated corners.