Free electron model

About: Free electron model is a research topic. Over the lifetime, 4678 publications have been published within this topic receiving 103535 citations.

Formation and decay of C−60 following free electron capture by C60

Abstract: The results of a detailed crossed electron/molecular beam study of electron attachment to C60 molecules and electron detachment from C−60 over the range of electron energies from near zero to about 15 eV are described. It is shown by comparing the experimental data for the attachment cross sections (normalized to the absolute thermal cross sections determined using the flowing afterglow/Langmuir probe apparatus) with quantum calculations that attachment occurs at low energies in the p‐wave channel, and in the d‐ and f‐wave channels (and probably higher‐order partial waves) at the higher electron energies. At electron energies above 7 eV, thermal detachment of electrons from the hot C−60 negative ions is seen to occur, and the unimolecular rate coefficients for detachment, kd, have been determined as a function of the energy of the attaching electron. Hence, by relating kd to the derived temperature of the hot C−60 ions, the electron detachment energy, Ed, has been determined as 2.6 eV, which is close to t...

Metallic non-Fermi-liquid fixed point in two and higher dimensions

Abstract: Quasi-one-dimensional electron systems in two and higher dimensions are studied. It is shown that the interchain electron hopping is renormalized to zero in the infrared limit if the intrachain repulsive interaction is strong enough. In this case the higher-dimensional electron system flows to metallic non-Fermi-liquid fixed points---a Luttinger liquid. Some experimental consequences, in particular the transport properties, of this infrared fixed point are studied. It would be interesting to observe this state in quasi-one-dimensional electron systems.

Quantization of coupled orbits in metals II. The two-dimensional network, with special reference to the properties of zinc

Abstract: In an earlier paper the wave functions and eigenvalues for an electron moving in a magnetic field, and interacting with one component of lattice potential, were analysed in terms of a model of coupled localized orbits. The model is now examined in more detail and shown to be a reasonable approximation to one possible representation of the true wave function. It is then extended to cover the case of a two-dimensional metal, the model now consisting of a network of interlocking orbits, on which an electron can move with specified probability amplitude for making a transition between orbits at any junction point. The problem of periodicity of the structure is discussed carefully, and it is found that the phase changes accompanying gauge transformations assume great importance. It is shown that the magnetic field imposes a periodicity on the network which is not in general compatible with that of the lattice potential, and the consequences are briefly investigated with the conclusion that they are probably observable only with difficulty. A special case, the hexagonal network, is then solved exactly, the magnetic field being chosen to avoid the above mentioned difficulty of incompatible periodicities. From the solution an energy level diagram is constructed, showing how the free-electron levels are broadened by the lattice potential and, as this is made stronger, reconstruct themselves into the sharp level system predicted by Onsager’s semi-classical method. In the intermediate stages of the process the bands contact each other frequently and other types of singularity appear. It is claimed that the structure revealed by this simple model is more elaborate than anything that could be readily derived by a perturbation treatment of the magnetic field. The electrons are able to move as quasi-particles in straight lines in any direction through the lattice, the velocity being derived from the energy level structure by the standard formula h~x^ kE.. When the bands are at their broadest the velocity is comparable with that of a free electron near the corners of the Brillouin zone. The contribution of the quasiparticles to the conductivity of the metal is evaluated on the assumption that the width of individual bands is rather less than kT ,so that much of the rapid variation of conductivity with Fermi energy is smoothed out. The variations that are left are still considerable and have a periodicity determined by the smallest quantized orbits. The results of the theory are applied to the fairly extensive, though not always consistent,observations of oscillatory behaviour in zinc. The anomalous variation with field strength of the de Haas-van Alphen amplitude can be satisfactorily explained if it is assumed that the energy gap across the sides of the Brillouin zone is about 0.027 eV. The vigorous resistance oscillations, attributed by Stark to magnetic breakdown changing some of the hole orbits into electron orbits, are shown to require more than this, though this effect is certainly important and is implied by the theory. It is suggested that the quasi-particles provide the necessary extra mechanism to account for resistance and Hall-effect data, but quantitative comparison is far from satisfactory, and it is concluded that more data and further analysis are probably needed. Stark’s proposal that the fine structure of the oscillations are due to spin, with a g -factor of 34, is disputed since it appears that the quasi-particle conductivity possesses the right sort of fine structure to account for the observations.

Optical spectroscopy of extrinsic recombinations in gallium selenide

Abstract: Luminescence at energy lower than the absorption edge has been investigated in crystals of GaSe, containing different degrees of lattice disorder, as a function of temperature, of photoexcitation intensity, and of excitation energy. At low excitation intensity, the extrinsic luminescence is composed of broad overlapping bands that present a blue shift when the temperature increases. Their shape and intensity is strongly dependent on the laser excitation frequency and on the degree of lattice disorder. The results are discussed in terms of a model involving the recombination of shallow donors and free electrons with deep acceptors. These two recombination mechanisms and those involving free and bound excitons are found to be competitive. Their relative importance is strongly dependent on the concentration of structural defects, on the temperature, on the excitation intensity, and on the excitation frequency.