CPM Seminar

We calculate the linear response function in configuration space for the system of electrons in an impurity band of a doped semiconductor. We assume that the impurity concentration n is within an intermediate range, where there are no free carriers in the conduction band or the valence band at low T, so that all charge carriers belong to the inpurity band. Since disorder in the spatial distribution of substitutional impurities is an essential ingredient of the model, we generate a completely random distribution of impurities within the given volume of the system. The only restriction imposed is that their wave functions, assumed to be the hydrogenic ground state ones obtained within the effective mass approximation, do not overlap. We also assume that some localized magnetic moments are distributed in the system. Then an indirect exchange interaction arises among different spins due to the spin fluctuations of the impurity band. In second order, as in the RKKY theory, the effective exchange integral for spins at distance R is proportional to the linear response function in configuration space, X(R).

We obtain, within the tight-binding approximation, the Green function for impurity band electrons at distance R, and consequentely the response function, by directly diagonalizing the tight-binding Hamiltonian for clusters of up to 1000 impurities, and we average X(R) over different random configurations. The results for the averaged X(R) show oscillating behaviour, with amplitude decreasing with distance like R^-3. The wavelength of the oscillation scales with the mean impurity separation, n^-1/3. We discuss possible realizations of the model.

Thursday, November 15th 2001, 16:00
Ernest Rutherford Physics Building, room 115