Localization in non-Hermitian asymmetric rhombic lattice

We propose a non-Hermitian rhombic lattice and investigate the Aharonov-Bohm caging, which forms at the exceptional point (EP) of the rhombic lattice at which all the lattice eigenstates are coalesced. The compact localized eigenstates and the localization dynamics are investigated. The excitation intensity can be constant or can polynomially increase with time as a consequence of the peculiar dynamics at the EP. The excitation can be completely localized in the two diamond plaquettes of the rhombic lattices and the localization area can be controlled by the gain and loss. Our findings shed light on the Aharonov-Bohm cage in the non-Hermitian physics and are beneficial for light engineering in the non-Hermitian metamaterials.