Observation of Riemannian geometric effects on electronic states

¹ Research Laboratory for Nuclear Reactors and Department of Nuclear Engineering, Tokyo Institute of Technology O-okayama, Meguro, Tokyo 152-8550, Japan
² Department of Materials Science, Nagoya University - Chikusa, Nagoya 464-8603, Japan
³ Division of Applied Physics, Faculty of Engineering, Hokkaido University - Sapporo, Hokkaido 060-8628, Japan
⁴ Department of Environmental Sciences and Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi - 4-4-37, Takeda, Kofu, Yamanashi 400-8510, Japan
⁵ Department of Physics, Nara Women's University - Nara 630-8506, Japan
⁶ UVSOR Facility, Institute for Molecular Science, and School of Physical Sciences, The Graduate University for Advanced Studies (SOKENDAI) - Okazaki, Aichi 444-8585, Japan

^a jonoe@nr.titech.ac.jp

Received: 6 March 2012
Accepted: 27 March 2012

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.