Engineering non-Hermitian Second Order Topological Insulator 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 quasi-crystalline lattice (QL). We first construct a non-Hermitian extension of the Bernevig-Hughes-Zhang (BHZ) model on a QL generated by the Amman-Beenker (AB) 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. Our findings pave a path to engineering exotic SOT phases where corner states can be localized at designated corners