R. J. Elliott

The intensity of optical absorption close to the edge in semiconductors is examined using band theory together with the effective-mass approximation for the excitons. Direct transitions which occur when the band extrema on either side of the forbidden gap are at the same K, give a line spectrum and a continuous absorption of characteristically different form and intensity, according as transitions between band states at the extrema are allowed or forbidden. If the extrema are at different K values, indirect transitions involving phonons occur, giving absorption proportional to ${(\ensuremath{\Delta}E)}^{\frac{1}{2}}$ for each exciton band, and to ${(\ensuremath{\Delta}E)}^{2}$ for the continuum. The experimental results on ${\mathrm{Cu}}_{2}$O and Ge are in good qualitative agreement with direct forbidden and indirect transitions, respectively.

We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties---optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

The fundamental relationship between radiative lifetime and spectral linewidth of free excitons is demonstrated theoretically and experimentally for quasi 2D excitons in GaAs/AlGaAs quantum wells.Received 24 August 1987DOI:https://doi.org/10.1103/PhysRevLett.59.2337©1987 American Physical Society

The incoherent inelastic scattering cross section of slow neutrons from liquids is calculated using a simple model in which the liquid is assumed to have appreciable short range order in a quasi-crystalline form. Diffusive motion takes place in large discrete jumps, between which the atoms oscillate as in a solid. The model predicts a definite, easily calculable cross section which is not dominated by diffusion effects as when continuous diffusion is assumed, but shows a characteristic variation with angle which could be looked for experimentally. The related pair correlation functions are dominated at small r and t by vibrational effects. Although simple and extreme the model explains several aspects of the observations of Brockhouse and Pope in 1959 and others. A brief discussion of the coherent scattering cross sections for the model is given although explicit formulae are not obtained.