Localized nonlinear vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

► Exact localized nonlinear vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities are reported. ► An infinite number of exact vector pairs sharing the same chemical potential are presented. ► The stable vortex-vortex pairs (±l,±l) with large topological charges can be supported in this system.