P. Clarke describes mirror symmetry as a duality between Landau-Ginzburg models, so that the dual of an LG model is another LG model. We describe examples in which the underlying space is a total space of a vector bundle on the projective line, and we show that self-duality occurs in precisely two cases: the cotangent bundle and the resolved conifold.
"Self-Duality for Landau--Ginzburg Models." J. Geom. Symmetry Phys. 35 1 - 10, 2014. https://doi.org/10.7546/jgsp-35-2014-1-10