Impurity levels of electrons in 2D structures formed by magnetic edge states

The bound states at the impurity center arising in a two-dimensional electron gas in a strong transverse magnetic field, taking into account the influence of the sample boundaries, are theoretically investigated. In the edge states, one component of the electron momentum is preserved, i. e. the motion becomes effectively one-dimensional. Using the example of a band of finite width, an equation is obtained that determines the energy of the impurity state and is a generalization of the known result for a shallow potential well in a one-dimensional system in the case of an arbitrary law of dispersion. The energies of the impurity levels belonging to the zero magnetic subzone are numerically found.