  Bloch-Zener oscillations (BZO), i.e. the interplay between Bloch oscillations
and Zener tunneling in two-band lattices under an external dc force, are
ubiquitous in different areas of wave physics, including photonics. While in
Hermitian systems such oscillations are rather generally aperiodic and only
accidentally periodic, in non-Hermitian (NH) lattices BZO can show a transition
from aperiodic to periodic as a NH parameter in the system is varied.
Remarkably, the phase transition can be either smooth or sharp, contrary to
other types of NH phase transitions which are universally sharp. A
discrete-time photonic quantum walk on a synthetic lattice is suggested for an
experimental observation of smooth BZO phase transitions.
