Sliding is a ubiquitous phenomenon in moir\'e systems, but its direct influence on moir\'e bands, especially in multi-twist moir\'e systems, has been largely overlooked to date. Here, we theoretically show that sliding provides a unique pathway to engineer the quantum geometry (Berry curvature and quantum metric) of moir\'e bands, exhibiting distinct advantages over conventional strategies. Specifically, we first suggest alternating twisted trilayer MoTe2 (AT3L-MoTe2) and chirally twisted triple bilayer graphene (CT3BLG) as two ideal paradigmatic systems for probing sliding-engineered quantum geometric phenomena. Then, two sliding-induced exotic quantum geometry phenomena are predicted: (1) an intrinsic nonlinear Hall effect via sliding-produced non-zero Berry curvature dipole, with CT3BLG as an ideal platform; (2) significant quantum metric modulation in AT3L-MoTe2, enabling tests of quantum geometric criteria for fractional Chern insulating state (FCIS). Our work establishes sliding as a new degree of freedom for manipulating quantum geometry of moir\'e bands, which emerges as a signature phenomenon of multi-twist moir\'e systems.
@article{arxiv.2509.09077,
title = {Sliding-tuned Quantum Geometry in Moir\'e Systems: Nonlinear Hall Effect and Quantum Metric Control},
author = {Shi-Ping Ding and Miao Liang and Tian-Le Wu and Meng-Hao Wu and Jing-Tao Lü and Jin-Hua Gao and X. C. Xie},
journal= {arXiv preprint arXiv:2509.09077},
year = {2025}
}