  We first prove that the K-theoretic Hall algebra of a preprojective algebra
of affine type is isomorphic to the positive half of a quantum toroidal quantum
group. An essential step consists to deform the K-theoretic Hall algebra so
that the deformation is torsion free over some polynomial subalgebra. Next, we
compare super toroidal quantum groups of type A with K-theoretic Hall algebras
of quivers with potential, which are defined using the Grothendieck groups of
categories of singularities of some Landau-Ginzburg models.
