New examples of zero modes

We construct smooth vector potentials A(1) and A(2) on Bbb R3 such that the associated Pauli operators scenterdot(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 L2. The second example can be written in the form A(2) = (-x2,x1,0)T + tilde A(2) where tilde A(2) is bounded and supported on {|x3|=1}. Furthermore the associated zero mode is Schwartz class.