New examples of zero modes

We construct smooth vector potentials A((1)) and A((2)) On R-3 such that the associated Pauli operators sigma bullet>(*) over bar * (D - A((i))), i = 1,2, have zero-energy eigenfunctions (or zero modes). The first example A((1)) has compact support and the associated zero mode is contained in L-2 The second example can be written in the form A((2)) = (-x(2), x(1), 0)(T) +(A) over tilde ((2)) where (A) over tilde ((2)) is bounded and supported on {\x3\ less than or equal to 1}. Furthermore the associated zero mode is Schwartz class.