  We investigate the energy spectral phase transitions arising in
one-dimensional superlattices under an imaginary gauge field and possessing M
sites in each unit cell in the large M limit. It is shown that in models
displaying nearly flat bands a smooth phase transition, from quasi entirely
real to complex energies, can be observed as the imaginary gauge field is
increased, and that the phase transition becomes sharper and sharper (exact) as
M is increased. In this limiting case, for superlattices with random or
incommensurate disorder the spectral phase transition corresponds to a
localization-delocalization transition of the eigenfunctions within each unit
cell, dubbed nonHermitian delocalization transition and originally predicted by
Hatano and Nelson. However, it is shown here that in superlattices without
disorder a spectral phase transition can be observed as well, which does not
correspond to a non-Hermitian delocalization phase transition. The predicted
phenomena could be observed in non-Hermitian photonic quantum walks, where
synthetic superlattices with controllable M and imaginary gauge fields can be
realized with existing experimental apparatus.
