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arXiv:2205.11462 · Physical Review X

Discovery of a Single-Band Mott Insulator in a van der Waals Flat-Band Compound

Shunye Gao, Shuai Zhang, Cuixiang Wang, Shaohua Yan, Xin Hai Han, Xuecong Ji, Wei Tao, Jingtong Liu, Tiantian Wang, Shuaikang Yuan, Gexing Qu, Ziyan Chen, Yongzhao Zhang, Jierui Huang, Mojun Pan, Shiyu Peng, Yong Hu, Hang Li, Yaobo Huang, Hui Zhou, Sheng Meng, Liu Yang, Zhiwei Wang, Yugui Yao, Zhiguo Chen, M. Shi, Hong Q. Ding, Huaixin Yang, Kun Jiang, Yunliang Li, Hechang Lei, Youguo Shi, Hongming Weng, Tian Qian

Published Dec 13, 2023• 66 citations
arXivHTMLPDF

Abstract

The fundamental model for understanding Mott insulators is the single-band Hubbard model. An ideal realization of that model arises in Nb${}_{3}$Cl${}_{8}$, proving a powerful system for exploring Mott physics and other correlated states.

DOI
10.1103/physrevx.13.041049

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The fundamental model for understanding Mott insulators is the single-band Hubbard model. An ideal realization of that model arises in Nb3{}_{3}3​Cl8{}_{8}8​, proving a powerful system for exploring Mott physics and other correlated states.
Motivated by recent experiments realizing correlated phenomena and superconductivity in two-dimensional (2D) van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model and a partially flat-band structure containing a nondispersing region, with identical total noninteracting bandwidth Wtot{W}_{\mathrm{tot}}Wtot​. For both repulsive and attractive weak interactions ($|U|\ensuremath{\ll}{W}_{\mathrm{tot}}$), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with UUU being an order of magnitude smaller than Wtot{W}_{\mathrm{tot}}Wtot​, we find the presence of a Mott insulating state near half filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the noninteracting electronic dispersion.
We report 10 ground states arising from strong correlations in the single-orbital Hubbard model on the decorated honeycomb lattice, including Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and trimer Mott insulators, and a spin-1 Mott insulator. The rich phase diagram arises from structures within the unit cell. Hence, such states are absent on simpler lattices. We argue that such insulating phases are prevalent on decorated lattices. These are found in many materials and common in coordination polymers, providing a playground to explore this physics.
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.