18 May 2021 Tue 5 pm

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Flat bands are known to naturally arise in a class of geometrically frustrated lattices like kagome, pyrochlore and checkerboard lattices, which are well understood based on the line graph theory and its analogues[1]. Recently, there had been several ideas to introduce a finite topological Chern number to these flat bands, e.g. by adding a small spin-orbit coupling (SOC). However, when the band becomes topological it immediately loses the perfect flatness, and fall into the category of "nearly-flat-bands".

In this work[2], we show that the large SOC can realize a perfect flat band, which is contour-intuitive in the context of previous studies. We construct a spinor-line-graph theory which proves the existence of perfect flat band when the SU(2) hopping parameter takes some particular value. We particularly focus on the pyrochlore lattice as a realistic example, with in mind a beta-pyrochlore oxide CsW2O6. In analogy to the emergent ferromagnetism of the standard flat bands in line-graph Hubbard models[1], our SOC-induced flat band gives a trimerized charge ordering when an infinitesimally small Coulomb interaction U is introduced.

This will explain the exotic trimerized phase of the material recently reported in the experiment[3].

[1] A. Mielke, J. Phys. A: Math. Gen. 24, 3311 (1991); H. Tasaki, Phys. Rev. Lett. 69, 1608 (1992).

[2] Hiroki Nakai and Chisa Hotta, arXiv:2103.13672 (2021).

[3] Y. Okamoto, H. Amano, N. Katayama, H. Sawa, K. Niki, R. Mitoka, H. Harima, T.

Hasegawa, N. Ogita, Y. Tanaka, M. Takigawa, Y. Yokoyama, K. Takehana, Y. Imanaka, Y.

Nakamura, H. Kishida, K. Takenaka, Nature Comm. 11, 3144(2020).