The present disclosure concerns a method of fabricating a curved 2D membrane comprising providing a curved polymer template on a support, flowing a solution of 2D material through the curved polymer template in order to form 2D multilayers on the curved polymer template and separating the 2D multilayers from the curved polymer template in order to form the curved 2D membrane. The curved 2D membrane is 10 characterised by a hyperbolic paraboloid curvature. The curved 2D membrane is characterised by a multi-layered lamellar morphology.