Influence of a Magnetic Field and an off-center Impurity on the Electron Energy Spectrum in a Spherical Multilayer Nanosystem

The influence of a constant magnetic field and the position of a shallow donor impurity on the energy spectrum of an electron and its probability density distribution in a spherical AlxGa1-xAs/GaAs/AlxGa1-xAs nanosystem has been studied. In the approximation of the effective mass and the model of rectangular wells and barriers, the solutions of the Schrödinger equation have been obtained by the expansion of the ground and excited state wave functions of an electron on the basis of the exact wave functions in the absence of a magnetic field and an impurity have been found. It has been shown that with increasing magnetic field induction, the role of the electron ground state in the nanosystem without impurities is consistently performed by the states with the magnetic quantum number m ( 0, – 1, – 2, ... (the Aharonov-Bohm effect). It has been established that the period of such oscillations of the electron ground state does not depend on the potential barriers height. However, the presence of an off-central donor impurity located in a potential well of the nanosystem, results in the vanishing of the Aharonov-Bohm effect. The dependences of the electron energy spectrum and wave functions on the position of an impurity shifted from the nanosystem center along and perpendicular to the magnetic field direction have been obtained. It has been shown that in the first case, the quantum states are characterized by a certain value of the magnetic quantum number m, and the expansion contains only wave functions of states with this value of m. In the second case, the problem loses cylindrical symmetry and new quantum states are formed from the states with different values of all three quantum numbers n, l, m.