Nonorientability-induced PT phase transition in ladder lattices

Abstract

We study parity-time (PT) phase transitions in the energy spectra of ladder lattices caused by the interplay between nonorientability and non-Hermitian PT symmetry. The energy spectra show level crossings in circular ladder lattices with increasing on-site energy gain-loss because of the orientability of a normal strip. However, the energy levels show PT phase transitions instead of the avoided level crossings of a Hermitian situation in PT-symmetric Mobius ladder lattices due to the nonorientability of a Mobius strip. The latter effectively presents a perturbation that would cause avoided level crossing in a Hermitian situation, but leads, in the presence of PT symmetry, to locked real energy parts and conjugate values of the imaginary parts. In order to understand the level crossings of PT-symmetric phases, we generalize the rotational transformation using a complex rotation angle. We also study the modification of resonant tunneling induced by a sharply twisted interface in PT-symmetric ladder lattices. Finally, we find that perfect transmissions at the zero energy are recovered at the exceptional points of the PT-symmetric system due to the self-orthogonal states.