Thesis (Ph.D.) - University of St Andrews, November 2008.

No description available.

Variational method is used to investigate, at zero temperature, the deformed- Fermi-surfaces mechanism for solving the problem of superconducting pairing of two species of fermions (i.e., spin-up and -down) of mismatched Fermi surfaces due to the existence of a uniform exchange or Zeeman field. After analyzing the depairing regions in the whole three-dimensional parameter space, we obtain a trial groundstate wave-function as a function of the three variational parameters, one of which is the gap function. Then within the frame work of the weak-coupling BCS theory, the expectation value of the Hamiltonian of a conductor under an exchange or Zeeman field is derived, from which a gap equation is derived by differentiation. The influence of deformed Fermi surfaces on the chemical potential is then calculated. Computer programing is finally used to solve the gap equation, and find the minimum-energy state with respect to the remaining two variational parameters (δµ and z). These two parameters are better than the original parameters used in the trial Hamiltonian when compared with the FF state. And we also found if we keep the total number of electrons fixed, the system prefers an unchanged chemical potential and the ground state energy of the deformed-Fermi-surfaces state, which is found to be an angle dependent case of Sarma’s solution III, is no better than that of the unpolarized BCS state.

Variational method is used to investigate, at zero temperature, the deformed- Fermi-surfaces mechanism for solving the problem of superconducting pairing of two species of fermions (i.e., spin-up and -down) of mismatched Fermi surfaces due to the existence of a uniform exchange or Zeeman field. After analyzing the depairing regions in the whole three-dimensional parameter space, we obtain a trial groundstate wave-function as a function of the three variational parameters, one of which is the gap function. Then within the frame work of the weak-coupling BCS theory, the expectation value of the Hamiltonian of a conductor under an exchange or Zeeman field is derived, from which a gap equation is derived by differentiation. The influence of deformed Fermi surfaces on the chemical potential is then calculated. Computer programing is finally used to solve the gap equation, and find the minimum-energy state with respect to the remaining two variational parameters (δμ and z). These two parameters are better than the original parameters used in the trial Hamiltonian when compared with the FF state. And we also found if we keep the total number of electrons fixed, the system prefers an unchanged chemical potential and the ground state energy of the deformed-Fermi-surfaces state, which is found to be an angle dependent case of Sarma's solution III, is no better than that of the unpolarized BCS state.

No description available.

No description available.

Experimental studies of optical properties in undoped and modulation-doped v-groove quantum wires (QWR) are presented. The results show good agreement with theoretical predictions. The investigation of undoped samples demonstrates the successful fabrication of high quality samples with small wire dimensions, exhibiting narrow linewidths and large subband spacings. Calculations from the Schrodinger solver show good agreement with the experimental results. Information about the shape of the confining potential is obtained from magneto-optical measurements where anisotropic shrinkage and binding energies of the excitons are measured. In high excitation power experiments the suppression of the excitonic recombination is observed due to screening and phase space filling. Photoluminescence excitation experiments reveal an inefficient carrier intersubband relaxation. Extending the optical investigations to modulation-doped samples, the formation of a one-dimensional electron gas can be observed. As a strong indication for this is the presence of a Fermi edge singularity (FES). Furthermore, Poisson-Schrodinger calculations show that the increased electron density in the conduction band leads to modified confinement energies. This was confirmed in magneto photoluminescence (MPL) experiments, where the diamagnetic shift of the luminescence from the first excited state is stronger than in the undoped case, as the state is squeezed further into the corners of the QWR. Recombination of the ground state electrons with different hole states appears as a fine structure in MPL spectra. Detailed analysis provides clear evidence of the FES. The expected temperature sensitivity of the FES is observed for lattice and electron heating. The FES intensity is also reduced at high excitation powers. The role of hole localisation and subband coupling is discussed. At applied magnetic fields the coupling of bands induces an enhancement of the singularity. Finally, the behaviour of hot carriers is investigated with time-resolved and electro-photoluminescence measurements. Long luminescence lifetimes indicate that electron-hole separation occurs due to the pinch-off between the QWR and the side quantum well. The field dependence of the electron heating shows quite clearly that LO phonon scattering is the dominant relaxation process at electron temperatures above ~40 K.

Th.--Sci. phys.--Nancy--I.N.P.L., 1977.

A study of the Fermi surface of copper at room temperature has been made by means of a positron annihilation technique. A positron active copper single crystal was placed midway between two “point" scintillation counters operated in time coincidence. The coincidence count rate was measured for various crystal orientations and the count rate interpreted as a measure of the diameter of the Fermi surface. The experiment yields a Fermi surface that is spherical in k-space except for protrusions in the {111} directions which are estimated to subtend an angle of about 20° at k = 0. Within experimental error the results are consistent with those obtained by other methods near 0° K. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A positron annihilation experiment involving collinear point geometry is used to make a direct comparison of the k₁₁₀ and k₁₀₀ Fermi radii in a single crystal of lithium. It is found that is k₁₁₀ greater than k₁₀₀ by 5.6 ± 1.2%, in agreement with theory and a phenomenological interpretation of an earlier long slit experiment. The higher momentum components of the positron wavefunction are calculated by a direct method and found to be negligible. On the other hand, a less straightforward estimate based on a flattened Seitz potential shows that the higher momentum components of the electron wavefunction significantly reduce the experimentally observed anisotropy. Hence, the difference of 5.6% should be regarded as an upper limit on the true distortion of the Fermi surface of lithium. / Science, Faculty of / Physics and Astronomy, Department of / Graduate