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Noncentrosymmetric metals are anticipated to exhibit a $dc$ photocurrent inthe nonlinear optical response caused by the Berry curvature dipole in momentumspace. Weyl semimetals (WSMs) are expected to be excellent candidates forobserving these nonlinear effects because they carry a large Berry curvatureconcentrated in small regions, i.e., near the Weyl points. We have implementedthe semiclassical Berry curvature dipole formalism into an $ab~initio$ schemeand investigated the second-order nonlinear response for two representativegroups of materials: the TaAs-family type-I WSMs and MoTe$_2$-family type-IIWSMs. Both types of WSMs exhibited a Berry curvature dipole, in which type-IIWeyl points are usually superior to the type-I because of the strong tilt.Corresponding nonlinear susceptibilities in several materials promise anonlinear Hall effect in the $dc$ field limit, which is within theexperimentally detectable range.

The Berry curvature dipole in Weyl semimetal materials: an ab initio study