Topological electronics: from infinity to six

Abstract

Topology captures the essence of what remains unchanged under a transformation. This study was motivated by a newly found topological invariant called super conformality that leads to local activity of a higher-integral-order electric element. As a result, the traditional periodic table of the electric elements can be dramatically reduced to have only six passive ones (resistor, inductor, capacitor, memristor, meminductor, and memcapacitor), in contrast to the unbounded table predicted 40 years ago. Our claim was experimentally verified by the fact that the two higher-integral-order memristors in the famous Hodgkin–Huxley circuit are locally active with an internal battery.