  We study parity-time (PT) phase transitions in the energy spectra of ladder
lattices caused by the interplay between non-orientability 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 in
PT-symmetric Moebius ladder lattices due to the non-orientability of a Moebius
strip. 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 the perfect
transmissions at the zero energy are recovered at the exceptional points of the
PT-symmetric system due to the self-orthogonal states.
