Observation of Riemannian geometric effects on electronic states

Abstract

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. Whether or not Riemannian space affects the electronic properties of condensed matters on a much smaller scale is of great interest. 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 first observation of Riemannian geometrical effects on the electronic properties of materials such as Tomononaga-Luttinger liquids, which were previously theoretically predicted by our group. We present in situ high-resolution ultraviolet photoemission spectra of a one-dimensional metallic C60 polymer with an uneven periodic peanut-shaped structure.