  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 the
chiral symmetry. Skin states are formed when the system is nonreciprocal, where
it is said nonreciprocal if the absolute values of the right- and left-going
hoppings amplitudes are different. Indeed, the zero-energy edge modes emerge at
both edges in the topological phase of the 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 the nonreciprocal
(reciprocal) non-Hermitian topological systems. Topological phase transitions
are observable by measuring the impedance resonance due to zero-admittance
topological corner modes.
