Topolectrical Circuits

By Ching Hua Lee, Stefan Imhof, C. Berger, F. Bayer, J. Brehm, L. Molenkamp, T. Kießling, R. Thomale. Communications Physics, 2017

600 citations recorded by the source corpus.

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.The discovery of topological insulators has given rise to a flourishing field dedicated to the investigation of the topological state of matter. This manuscript contributes to this field by introducing the idea of a topoelectrical circuit, whereby an assembly of conventional circuit elements realises various topological band structures.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/d8967aab2fe2ce771b582651aa4b9d7d7056df87

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Topological photonics (2018, methodology): “The SSH model has also been realized with electric circuits (Lee et al., 2018), and the Zak phase (Berry phase across the Brillouin zone) has been measured to show its topological nature (Goren et al., 2018).”
Impurity induced scale-free localization (2020, methodology): “To isolate a particular λ′-th eigenmode, we tune the circuit until λ′ ≈ 0, either by adjusting its variable components or by varying the AC frequency ω [45].”
Perspective on topological states of non-Hermitian lattices (2019, methodology): “on is used after mapping to a Schrodinger-like equation, as in systems with gain and¨ loss (as found in optics and photonics [33, 34, 35, 36]), surface Maxwell waves [37], and topoelectrical circuits [38, 39]. Topological effects are intrinsic to features unique to non-Hermitian Hamiltonians such as”
Probing non-Hermitian skin effect and non-Bloch phase transitions (2019, background): “Our results are expected to stimulate further theoretical studies in a rapidly growing area of research and could provide insights into experimental observation of nonBloch phase transitions in photonic systems and topolectrical circuits, where non-Hermitian topological SSH models like the ones cons”
Reciprocal skin effect and its realization in a topolectrical circuit (2019, unknown): “where we defined Jab(ω) as the (grounded) circuit Laplacian [32].”