Stabilization of impurity states in crossed magnetic and electric fields

Abstract

It is shown that the renormalizability of the zero-range interaction in the two-dimensional space is always followed by the existence of a bound state, which is not true for odd-dimensional spaces. A renormalization procedure is defined and the exact retarded Green’s function for electrons moving in two dimensions and interacting with both crossed magnetic and electric fields and an attractive zero-range interaction is constructed. Imaginary parts of poles of this Green’s function determine lifetimes of quasibound (resonance) states. It is shown that for some particular parameters the stabilization against decay occurs even for strong electric fields.