Recent studies have shown that moir{e} flat bands in a twisted bilayer graphene(TBG) can acquire nontrivial Berry curvatures when aligned with hexagonal boron nitride substrate [1, 2], which can be manifested as a correlated Chern insulator near the 3/4 filling [3, 4]. In this work, we show that the large Berry curvatures in the moir{e} bands lead to strong nonlinear Hall(NLH) effect in a strained TBG with general filling factors. Under a weak uniaxial strain $sim 0.1%$, the Berry curvature dipole which characterizes the nonlinear Hall response can be as large as $sim$ 200{AA}, exceeding the values of all previously known nonlinear Hall materials [5-14] by two orders of magnitude. The dependence of the giant NLH effect as a function of electric gating, strain and twist angle is further investigated systematically. Importantly, we point out that the giant NLH effect appears generically for twist angle near the magic angle due to the strong susceptibility of nearly flat moir{e} bands to symmetry breaking induced by strains. Our results establish TBG as a practical platform for tunable NLH effect and novel transport phenomena driven by nontrivial Berry phases.
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