Abstract
Invented by Alessandro Volta and Félix 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. Here we show that topological insulating and semimetallic states can be realized in a periodic RLC circuit. 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 the TBR midgap state. 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.
Highlights
Invented by Alessandro Volta and Félix Savary in the early 19th century, circuits consisting of resistor, inductor and capacitor (RLC) components are omnipresent in modern technology
In an era where classical experimental setups for topological phases still need to improve in terms of uniformity of array elements, it is often challenging to resolve single edge mode responses to identify the onset of a topological insulator phase
We outline a detailed design of such topolectrical circuits, including a Weyl circuit network exhibiting Topological boundary resonances (TBRs) of Fermi arc type, where the AC driving frequency combined with the grounding design takes over the role of the chemical potential in a fermionic system
Summary
Secondary resonances are observed at larger deviations from ω~, and are associated with other eigenvalues of the grounded circuit Laplacian J. c Measurement of midgap voltage eigenmode ψ0(n), which accurately fits the shape predicted by theory, i.e., ψ0(n) = ((−t) nV0, 0) for the nth two-site unit cell from the left, see a for node numbering. Despite non-negligible serial resistance and element non-uniformities, the SSH midgap peak is observed in the impedance measurement but absent for the t−1 = 4.5 configuration network with two inequivalent nodes per unit cell, where unlike nodes are connected by capacitors of capacitances α, β, or γ depending on their relative orientations (Fig. 3a). Along these Fermi arcs, we recover the line nodes of the zig-zag topolectrical circuit, where the massive degeneracy is protected by sublattice symmetry
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