I am looking for a functor from varieties $X/\mathbf{Z}_p$ to $(\varphi,\Gamma)$-modules over the Robba ring over $\mathbf{Q}_p$ (overconvergent ones) that is contructed by differential methods (similar to log-crystaline cohomology) not by Galois methods and a twist by a Fontaine ring (would like to avoid, if possible, the use of the field of norms).