Invented by Alessandro Volta and F\'elix Savary in the early 19th century,
circuits consisting of resistor, inductor and capacitor (RLC) components are
omnipresent in modern technology. The behavior of an RLC circuit is governed by
its circuit Laplacian, which is analogous to the Hamiltonian describing the
energetics of a physical system. We show that topological semimetal band
structures can be realized as admittance bands in a periodic RLC circuit, where
we employ the grounding to adjust the spectral position of the bands similar to
the chemical potential in a material. Topological boundary resonances (TBRs)
appear in the impedance read-out of a topolectrical circuit, providing a robust
signal for the presence of topological admittance bands. For experimental
illustration, we build the Su-Schrieffer-Heeger circuit, where our impedance
measurement detects a TBR related to the midgap state. Due to the versatility
of electronic circuits, our topological semimetal construction can be
generalized to band structures with arbitrary lattice symmetry. Topolectrical
circuits establish a bridge between electrical engineering and topological
states of matter, where the accessibility, scalability, and operability of
electronics synergizes with the intricate boundary properties of topological
phases.Comment: 11 pages, 4 figure
