  We study the quantum nonlinear Hall effect in two-dimensional materials with
time-reversal symmetry. When only one mirror line exists, a transverse charge
current occurs in 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 $T_d$-stricture TMDCs exhibit a finite Berry
curvature dipole. In the $1H$ and $1T'$ phase of TMDCs, we show the emergence
of finite Berry curvature dipole with the application of strain and electrical
displacement field respectively.
