Spin–orbit interaction in a multilayered spherical quantum dot

The conventional spin–orbit interaction due to the presence of a central or off-central impurity located in a multilayered spherical quantum dot (MSQD) has been investigated. The different effective masses of dots and barriers have been taken into consideration. The spin–orbit interaction has been calculated in the excited state (2p). The variational method has been applied by using a new form of the trial wave function in addition to the conventional form that has been used in previous work. The new form has the advantage of satisfying the boundary conditions at the interfaces between dots and barriers in the case of different masses. The case of central impurity has been further explored by using the exact analytical solution in the state (2p) of the radial Schrödinger equation in the presence of the impurity. Moreover, the calculations have been performed in the case of a MSQD of thin inner barrier, for which the electron is most probably localized in the outer dot. Thus for an off-central impurity placed in the inner dot the spin–orbit energy increases continuously as the impurity location moves towards the surface of the inner dot. The study has yielded new analytical expressions for the electron energy, binding energy and spin–orbit expectation energy for both central and off-central impurities.