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We consider electronic intrasubband transitions involving the confined and interface optical phonons of circular and elliptical GaAs quantum wires. Detailed treatments are given for a GaAs wire embedded in AlAs where the electrons are confined via an infinite potential barrier. The optical phonons are described using the dielectric continuum (DC) model, which for the GaAs/AlAs system compares favourably with more sophisticated macroscopic models and ab initio microscopic calculations in its prediction for the total scattering rates. The DC model has been applied previously to the circular case, bur here we evaluate the rates analytically. It is shown that the behaviour of the electrons and phonons in elliptical wires is both quantitatively and qualitatively different from that in circular wires, especially as regards angular properties.

An exact calculation is given of the upper critical field of a hollow isotropic type-ll superconducting cylinder. This fieid is the analogue of the surface-sheath critical field H,, . As the temperature decreases below To the critical field corresponds to increasing values of the azimuthal quantum number Im 1 , i.e. the fluxoid number. The results are compared with those for a flat surface, a film and a solid cylinder and with the approximate result for a thin-walled cylinder. For the last case, it is shown how the Little-Parks oscillations are modified as the cylinder wall thickness increases. The effects of normai-metai cladding on the inner and outer surfaces are calculated. The critical temperature is reduced and the Little-Park oscillations become less pronounced.

The analogue of the surface nucleation field Hc3 is calculated for a superconducting cylinder in a magnetic field parallel to its axis. For small radius, on the scale of the coherence length, superconductivity nucleates uniformly across the cylinder, while for large radius a surface sheath nucleates at the outer perimeter, the bulk of the cylinder remaining normal. The transition between these two limits is seen as a succession of flux entry points each corresponding to an increase by unity in the magnitude of the fluxoid quantum number.

An investigation of the effects of a finite confining potential on the sub-band energies and electron-bulk-polar-optical-phonon scattering rates is presented within the effective-mass approximation for quasi-one-dimensional cylindrical quantum wires. Numerical results are given for the GaAs/AlGaAs system where a lowering of both the confined energies and electron-bulk-polar-optical-phonon scattering rates with respect to the widely used infinite-confining-potential approximation is found.