▎ 摘　　要

Exact analytic solutions for an electron in graphene interacting with external complex magnetic fields are found. The eigenvalue problem for the non-Hermitian Dirac-Weyl Hamiltonian leads to a pair of intertwined Schrodinger equations, which are solved by means of supersymmetric quantum mechanics. The Hamiltonian eigenstates turn out to be non-stationary, since their associated energy eigenvalues are complex, with the corresponding discrete spectrum thus defining the so-called Landau levels. By means of an analogy with non-uniform strained graphene, a prospective physical interpretation and a possible experimental situation, where the effects of the complex magnetic field could be detected, are given. The probability and current densities are explored and some remarkable differences as compared with the real case are discussed.