Engineering topolectrical circuits

Abstract

Topolectrical circuits are electrical networks that encode topological band theory. Their physical behaviour is set by how the components are wired together, not by where they are placed. This wiring-centred design delivers defect tolerance, directional signal flow without bulky magnetic parts, and amplified response at boundaries. Conventional electronics obtain these only by adding isolators, feedback or calibration after the circuit is laid out. In this Review, we identify which capabilities are engineering-ready and which remain confined to the laboratory. We cover the underlying physics, the resulting sensors and engineering applications, and cross-disciplinary uses in quantum simulation, artificial intelligence-assisted design and curved-space geometries. We then examine how co-integration with memristive devices makes the platform adaptive and history-dependent. We close with the hardware routes towards deployable electronics, from monolithic chips to flexible substrates and body-worn systems. Topolectrical circuits route signals one way without magnets and keep working when components fail. These capabilities come from how the components are wired together, not from added parts. This Review covers their physics, applications across sensing, wireless power and communications, and the path towards integrated, flexible and adaptive electronics.