Vortices and stabilization of resonance states in crossed magnetic and electric fields

We analyze a two-dimensional model of electrons moving under the influence of an attractive zero-range potential as well as external magnetic and electric fields. In order to determine the complex energies of the electron’s resonance states we use the Green’s-function method. It is found by numerical calculations that there are resonances that have a peculiar dependence on the electric-field intensity, i.e., although the electric field increases, the lifetime of these resonance states grows up. We show that this phenomenon, called stabilization, can be attributed to quantum-mechanical vortices induced by the magnetic field and controlled by the electric-field strength. In order to get more information about these vortices the phase of the wave functions as well as the probability currents for these stable resonances are investigated. We also demonstrate the existence of the so-called stabilization path.