Abstract
Time correlation functions are expanded in a hierarchical fractional form following Mori’s projection technique in a rigorous manner. Using this formula, detailed calculations are performed to obtain the cyclotron resonance lineshape function for an electron-phonon interaction system in both incoherent and coherent scattering regimes. We apply this formula to electron-acoustic phonon scattering systems. We carry out the calculation of the cyclotron resonance linewidths for purely two- and three-dimensional electrons in Ge and Si with an appropriate value of the fitting parameter and compare them. It is shown that, although the width increases with temperature in both cases, the width is smaller in two dimensions. This implies that the scattering is weaker in two dimensions. This is a physically reasonable result, and thus our result supports the validity of the theory.
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