  Line waves are recently discovered wave entities that are localized along two
directions, and therefore can be viewed as the one-dimensional counterpart of
surface waves. These waves can be supported at discontinuities of the surface
reactance and/or resistance of low-dimensional materials such as metasurfaces
or graphene. Here, a broader class of non-Hermitian surface-impedance junctions
is studied that can support coupled line waves, and allows investigating
different one-dimensional waveguiding mechanisms in a unified framework. It is
theoretically demonstrated that, under parity-time-symmetry conditions,
exceptional points can occur in a truly flat-optics scenario, hence endowing
these waveguiding systems with the attractive features of both line-wave and
exceptional-point physics, and shedding further light on the phase transitions
existing in these systems. It is also shown that the required surface-impedance
parameters are compatible with those attainable with typical models of
photoexcited graphene metasurfaces at terahertz frequencies. Besides providing
additional understanding in the physics of line waves, which is still in its
infancy, these results pave the way to intriguing developments in the largely
unexplored field of non-Hermitian flat optics, with possible applications
ranging from sensing to lasing and on-chip optical signal processing.
