Abstract

While the dispersion relation in band structures has long been regarded as a fundamental property of electrons in solids, the geometric structure of Bloch wave functions, encoded in the quantum geometric tensor, has recently emerged as a key ingredient of quantum materials. Although the imaginary part of the quantum geometric tensor, the Berry curvature, has been extensively studied, the role of the real part, the quantum metric, in correlated systems remains elusive.
I will discuss a perspective linking quantum geometry and many-body instabilities in interacting electron systems. It is demonstrated that the quantum metric directly controls electronic instabilities, giving rise to ferromagnetism [1,2], odd-parity multipole order [3], and spin-triplet superconductivity [1]. I will also show its crucial role in anomalous scaling laws of the superfluid weight of geometric origin [4].

[1] Taisei Kitamura, Akito Daido, Youichi Yanase, Phys. Rev. Lett. 132, 036001 (2024).
[2] Taisei Kitamura, Hiroki Nakai, Akito Daido, Youichi Yanase, arXiv:2505.01089.
[3] Kanta Kudo and Youichi Yanase, arXiv:2505.20907.
[4] Yuma Hirobe, Taisei Kitamura, Youichi Yanase, arXiv:2505.13065.