Dynamical signature of the moiré pattern in a non-Hermitian ladder

We study the dynamical behavior of a non-Hermitian moire superlattice system, which consists of two-coupled Su-Schrieffer-Heeger (SSH) chains with staggered imaginary on-site potentials. The slight difference, which indicates that the in-lattice spacing of nearest-neighbor lattice sites at the top is different from that in the bottom chain, can result in periodical occurrence of the two main spatial regions. We show that two such distinct regions are dimerized and tetramerized, which determine the distinct dynamical behaviors. The Dirac probability can oscillate periodically, increase quadratically, and increase exponentially, which correspond to the unbroken phase, exceptional points, and the broken phase of the tetramerized region. In comparison, the Dirac probability can exhibit high-frequency oscillation in the dimerized region. These phenomena demonstrate the dynamical signature and provide insightful information of the moire pattern in the non-Hermitian regime.