Topological Electronics: From Infinity to Six

TL;DR

This paper introduces a new topological invariant called super conformality that simplifies the periodic table of electric elements to only six passive types, supported by experimental verification of higher-order active elements.

Contribution

It discovers super conformality as a topological invariant and demonstrates its role in reducing the electric element periodic table to six passive types.

Findings

Super conformality preserves a critical angle in electric elements.

The periodic table of electric elements is reduced to six passive types.

Higher-order electric elements are shown to be active, confirmed experimentally.

Abstract

Topology captures the essence of what remains unchanged under a transformation. In this study, a topological invariant called super conformality was found to preserve a critical angle between the constitutive plane and its second order differential plane for a two-terminal electric element as building blocks of modern electronics. This super conformality leads to local activity of a higher-order electric element so that the periodic table of the electric elements can be dramatically reduced to have only 6 passive ones, in contrast to the unbounded table predicted 40 years ago. Our claim that all the higher-order electric elements must be active was experimentally verified by the fact that a 2nd-order sodium memristor in the famous Hodgkin-Huxley circuit is locally active with an internal battery.