Topological Circuits - A Stepping Stone in the Topological Revolution

Abstract

The 2016 Nobel prize in physics was awarded to the pioneers who studied topological systems in Condensed Matter Physics such as the Quantum Hall Effect, where edge currents in a material are restricted to discrete values. Topology was developed to study geometric structures where only global properties are of concern (like the number of holes in an object). It has since been applied to physical systems with remarkable success; such as circuit theory. In this project, Kirchhoff’s Laws are reformulated so that circuits can be analysed using the powerful tool of topology. This sheds light on the properties of exotic real materials such as graphene[24]. The quantum edge effect in a polyacetylene chain happens only when the edge of the chain is conducting. This was recreated experimentally using electrical circuits. Physical laws govern the properties of the bulk in a material to that of the edge. However, dissipation introduced into circuits using voltage controlled current sources was shown to have broken these laws. Results are attributed to boundary conditions affecting all states in the bulk, not just edge states, implying a new state of matter. Studying Condensed matter systems using electrical circuits gives physicists an accessible, scalable and inexpensive way to study real materials.