Topological Phase Transition in non-Hermitian Quasicrystals

The discovery of topological phases in non-Hermitian open classical and\nquantum systems challenges our current understanding of topological order.\nNon-Hermitian systems exhibit unique features with no counterparts in\ntopological Hermitian models, such as failure of the conventional bulk-boundary\ncorrespondence and non-Hermitian skin effect. Advances in the understanding of\nthe topological properties of non-Hermitian lattices with translational\ninvariance have been reported in several recent studies, however little is\nknown about non-Hermitian quasicrystals. Here we disclose topological phases in\na quasicrystal with parity-time ($\\mathcal{PT}$) symmetry, described by a\nnon-Hermitian extension of the Aubry-Andr\\'e-Harper model. It is shown that the\nmetal-insulating phase transition, observed at the $\\mathcal{PT}$ symmetry\nbreaking point, is of topological nature and can be expressed in terms of a\nwinding number. A photonic realization of a non-Hermitian quasicrystal is also\nsuggested.\n