Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A quantum ruler for orbital magnetism in moiré quantum matter



Marlou Slot, Yulia Maximenko, Paul M. Haney, Sungmin Kim, Daniel Walkup, Evgheni Strelcov, En-Min Shih, Dilek Yildiz, Steven R. Blankenship, Kenji Watanabe, Takashi Taniguchi, Yafis Barlas, Nikolai Zhitenev, Fereshte Ghahari Kermani, Joseph A. Stroscio


Topological properties that underlie the rich emergent phases of moiré quantum matter (MQM) result from the eigenstate geometry of the moiré Hamiltonian. The eigenstate geometry involves the Berry curvature and the less known quantum metric. Most studies to date have focused on measurements to identify the Chern topology in MQM, but did not characterize the quantum geometry in detail. For almost a century, magnetic oscillations have been a powerful "quantum ruler" for the analysis of Fermi surfaces. In this report, we use a quantum ruler of Landau levels to probe quantum geometry and topology in twisted double bilayer graphene. We demonstrate significant deviations from Onsager's relation due to anomalously large second-order magnetic susceptibility contributions, relying in part on the quantum metric, and exceeding first-order contributions from the Berry curvature. This breakdown is unique for the large lattice constants typical for MQM.
Science Magazine


Moire quantum matter, scanning tunneling microscopy, Landau levels


Slot, M. , Maximenko, Y. , Haney, P. , Kim, S. , Walkup, D. , Strelcov, E. , Shih, E. , Yildiz, D. , Blankenship, S. , Watanabe, K. , Taniguchi, T. , Barlas, Y. , Zhitenev, N. , Ghahari Kermani, F. and Stroscio, J. (2023), A quantum ruler for orbital magnetism in moiré quantum matter, Science Magazine, [online],, (Accessed June 18, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 5, 2023, Updated October 12, 2023