We study the quantum nonlinear Hall effect in two-dimensional (2D) materials with time-reversal symmetry. When only one mirror line exists, a transverse charge current occurs in the second-order response to an external electric field, as a result of the Berry curvature dipole in momentum space. Candidate 2D materials to observe this effect are two-dimensional transition metal dichalcogenides (TMDCs). First, we use an ab initio based tight-binding approach to demonstrate that monolayer Td-structure TMDCs exhibit a finite Berry curvature dipole. In the 1H and 1T′ phase of TMDCs, we show the emergence of a finite Berry curvature dipole with the application of strain and an electrical displacement field, respectively.
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We thank Inti Sodemann, Qiong Ma, Bertrand I. Halperin, Philip Kim, and Jeroen van den Brink for useful discussions. J.-S.Y. thanks Ulrike Nitzsche for technical assistance. This work was supported by the STC Center for Integrated Quantum Materials, NSF Grant No. DMR-1231319 and by ARO MURI Award No. W911NF-14-0247. The computations in this work were run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University.