One of the recent wisdom for topological phases is the use of a classical system as a quantum simulator. The Hofstadter butterfly associated with topological phase transitions is realized in electric circuits on a desktop. Electric circuits emulate the quantum Hall effect without following the physical law of the quantum world where not only the edges but also its bulk properties are both experimental observables. The Chern number due to the Streda formula and corresponding edge states are both experimentally measured to confirm the bulk-edge correspondence. The fractal structure of the Hofstadter diagram associated with higher Chern numbers is also directly measured. The paper is published in ”Observation of bulk-edge correspondence in topological pumping based on a tunable electric circuit”、Communications Physics, 5, Article number: 180 (2022), by Kenichi Yatsugi, Tsuneya Yoshida, Tomonari Mizoguchi, Yoshihito Kuno, Hideo Iizuka, Yukihiro Tadokoro, and Yasuhiro Hatsugai (published online on July 09, 2022).
The work is done in collaboration with researchers in Toyota Central R&D Labs.
See also News at Toyota Central R&D Labs in Japanese.