  Nonreciprocal transmission is the fundamental process behind unidirectional
wave propagation phenomena. In our work, a compact and practical parity-time
(PT) symmetric metamaterial is designed based on two Silicon Carbide (SiC)
media separated by an air gap and photonically doped with gain and loss
defects. We demonstrate that an exceptional point (EP) is formed in this
PT-symmetric system when SiC operates as a practical epsilon-near-zero (ENZ)
material and by taking into account its moderate optical loss. Furthermore and
even more importantly, strong self-induced nonreciprocal transmission is
excited due to the nonlinear Kerr effect at a frequency slightly shifted off
the EP but without breaking the PT-symmetric phase. The transmittance from one
direction is exactly unity while the transmittance from the other direction is
decreased to very low values, achieving very high optical isolation. The
proposed active nonlinear metamaterial overcomes the fundamental physical
bounds on nonreciprocity compared with a passive nonlinear nonreciprocal
resonator. The strong self-induced nonreciprocal transmission arises from the
extreme asymmetric field distribution achieved upon excitation from opposite
incident directions. The significant enhancement of the electric field in the
defects effectively decreases the required optical power to trigger the
presented nonlinear response. This work can have a plethora of applications,
such as nonreciprocal ultrathin coatings for the protection of sources or other
sensitive equipment from external pulsed signals, circulators, and isolators.
