Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization

A prominent feature of some one-dimensional non-Hermitian systems is that all right eigenstates of the non-Hermitian Hamiltonian are localized in one end of the chain. The topological and trivial phases are distinguished by the emergence of zero-energy modes within the skin states in the presence of chiral symmetry. Skin states are formed when the system is nonreciprocal, where it is said to be nonreciprocal if the absolute values of the right- and left-going hopping amplitudes are different. Indeed, zero-energy edge modes emerge at both edges in the topological phase of a reciprocal non-Hermitian system. Then, analyzing higher-order topological insulators in nonreciprocal systems, we find the emergence of topological zero-energy modes within the skin states formed in the vicinity of one corner. Explicitly, we explore the anisotropic honeycomb model in two dimensions and the diamond lattice model in three dimensions. We also study an electric-circuit realization of these systems. Electrical circuits with (without) diodes realize nonreciprocal (reciprocal) non-Hermitian topological systems. Topological phase transitions are observable by measuring the impedance resonance due to zero-admittance topological corner modes.