Theory of the Cyclotron Resonance in Al,Pb,Zn and Cd

A quantum theory of the cyclotron resonance is developed. For a face-centered-cubic (fcc) metal the obvious candidates for the Cyclotron Planes (CP) in which the conduction electron (``electron'',``hole'') circulates are the three families of planes $\{100\}$, $\{110\}$ and $\{111\}$. Following Dresselhaus-Kip-Kittel (DKK,1955) we assume a quadratic energy-momentum ($\hbar k$) relation with the effective mass $(m_{1},m_{2},m_{3})$ and analyze the angle- dependent resonance peaks in terms of Shockley's formula (a generalization of the DKK formula) .For aluminum Al (fcc) an ``electron'' ellipsoid with the major axes in [110] with $(m_1,m_2,m_3)=(0.108,0.156,1.96)m$ is obtained. For lead (Pb) (fcc) a hyperboloid in [110] with $(m_1,m_2,m_3)=(1.18,0.244,- 8.71)m$ and an ``electron'' sphere with $m^*=1.30m$ associated with the CP $\{100\}$ are obtained. For a hexagonal- closed-pack (hcp) metal,the CP is the hexagonal base plane. The effective mass $m_{b}$ for the basal-plane motion and the mass $m_{c}$ along the c-axis for zinc (Zn)[cadmium (Cd)] (both hcp)are $(m_{b},m_{c})$=(1.04,0.212)m [(1.14,0.217)m], which characterize the spheroids with the major axis along the c-axis.