Theory of the Angle-Dependent Cyclotron Resonance Peaks for Conducting Crystals

In the early fifties, Dresselhaus, Kip and Kittel (DKK) reported the first-ever observation of the cyclotron resonances for Ge and Si. They found the remarkable orientation -dependence of the resonance peaks and interpreted these data in terms of the well-known DKK formula for the cyclotron effective mass: ({1over m^* })^2 = {cos^2(mu, { rm x}_3)over m_sp{t }{2}} + {sin^2(mu, {rm x}_3)over m_{t } m_{l}},eqno(1) where rm (m_{t }, m_{l}) are transverse and longitudinal effective masses and cos (mu, {rm x}_3) represents the direction cosine between the magnetic field (direction mu) and the vertical (x_3) to the cyclotronic plane fixed in the crystals. In the present work I shall demonstrate that the anisotropic cyclotron resonance peak positions omega_{rm c} observed in semiconductor and metals can be analyzed in a unified manner, based on the Shockley's formula (generalized form of (1)): omega_sp{c} {2} = rm(qB)^2 {m_1 cos^2 (mu, x_1) + m_2cos^2 (mu, x_2) + m_3 cos^2 (mu, x_3)over m_1m_2m_3}, where q is the carrier charge, B is the magnetic field strength, and m_1, m_2 and m_3 are intrinsic masses, which are defined in connection with the equations of motion for the Bloch electron (wave packet). The intrinsic masses obtained by fitting the data yield a complete determination of the relevant part of the Fermi surface.