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Unlike a real magnetic field, which separates the energy levels of particlewith opposite spin polarization, a complex field can lead to a special kind ofspectral degeneracy, known as exceptional point (EP), at which two spineigenmodes coalesce. It allows an EP impurity to be an invisible scatteringcenter for a fermion with the resonant spin polarization, but an amplifyingemitter for opposite polarization. We show that a pair of conjugate EP modessupports resonant mutual stimulation, acting as a resonant amplifier based onthe underlying mechanism of positive-feedback loop. Together with otherHermitian eigenmodes, a fermion with EP polarization exhibits some exclusivedynamics, referred to as EP dynamics. We construct several typicalsuperlattices, which are built up by embedding EP-impurity arrays in aHermitian two-dimensional square lattice. Numerical simulations are performedto demonstrate resonant amplification and invisibility of Bragg scattering.

Resonant-amplified and invisible Bragg scattering based on spin coalescing modes