CYCLOTRON RESONANCE LINESHAPE OF FREE ELECTRONS

Ali M.H. AL-ARAB

This thesis is concerned with the theory of electron transport coefficients in  general and of the cyclotron resonance ac conductivity in particular.

We start from a general transport function R _{α β α 'β'} (t)from which all linear electron  transport coefficients can be derived.

 We use a time-evolution method to determine this transport function for a system in which the electrons interact with phonons. A suitable approximation is found by 'linearizing' certain higher order correlation functions. The result of this approximation procedure is that we obtain a transport equation for R _{α β α 'β}'  (t).

Two methods are used to solve this equation. The first is an improved version of that employed by several previous authors and effectively looks for a solution in a specific form. The second method attempts a direct numerical solution of the equation without further physical approximations.

The quantum limit cyclotron resonance lineshape and linewidth are considered in detail for the case of inelastic scattering by acoustic phonons via a deformation potential coupling in the high temperature range.

Calculations of the ac conductivity and of the linewidth show the following features:

         (a) The lineshape is almost symmetrical.

                 (b) The linewidth varies approximately proportional to the Temperature (T) and to the resonating magnetic field (B).