Riemannian Geometrical Effects on the Electronic Properties of Condensed Matters

Abstract

A. Einstein first applied Riemannian geometry to develop the general theory of relativity almost one hundred years ago and succeeded in understanding astronomical-scale phenomena such as the straining of time-space by a gravitational field. It is of great interest to reveal whether or not Riemannian geometry affects the electronic properties of condensed matters on a much smaller scale. Although Riemannian geometry has been applied to quantum mechanics since the 1950s, nobody has yet answered this question, because the electronic properties of materials with Riemannian geometry have not been examined experimentally. We report here the prediction and observation of Riemannian geometrical effects on the electronic properties of one-dimensional metallic uneven peanut-shaped C₆₀ polymer.