Potential automorphy of certain non self-dual 3-dimensional Galois representations

In a series of papers, van Geemen and Top have defined a family of surfaces Sz indexed by a nonzero integer parameter z, and a compatible family of 3-dimensional Galois representations over (i) attached to each surface. In this note we use recent advancements in potential automorphy and automorphy lifting to show that these compatible families are potentially automophic for all values of z, and hence that their L-functions have analytic continuation and a functional equation.