Zero-energy corner states in a non-Hermitian quadrupole insulator

We point out that in non-Hermitian systems, Jordan decomposition should replace eigendecomposition so all ``good approximate eigenstates'' of the system are identified. These states can be resonantly excited. As a concrete example, we study location and field distribution zero-energy corner quadrupole insulator (QI) split parameter space into three distinct regimes according to properties states: near-Hermitian QI, intermediate phase, trivial insulator. In newly discovered Hamiltonian becomes defective, counterintuitive delicate response external drives perfectly explained by decomposition.