  Non-Hermitian skin-edge states emerge only at one edge in one-dimensional
nonreciprocal chains, where all states are localized at the edge irrespective
of eigenvalues. The bulk topological number is the winding number associated
with the complex energy spectrum, which is well defined for metals. We study
non-Hermitian nonreciprocal systems in higher dimensions, and propose to
realize them with the use of electric diode circuits. We first investigate
one-dimensional interface states between two domains carrying different
topological numbers, where all states are localized at the interface. They are
a generalization of the skin-edge states. Then we generalize them into higher
dimensions. We show that there emerge a rich variety of boundary states and
interface states including surface, line and point states in three-dimensional
systems. They emerge at boundaries of several domains carrying different
topological numbers. The resulting systems are the first-order, second-order
and third-order topological metals. Such states may well be observed by
measuring the two-point impedance in diode circuits.
