Cyclotron Resonance in Metals with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>H</mml:mi></mml:math>Perpendicular to the Surface

Abstract

Explicit formulas are derived for the surface impedance of a single isotropic carrier in a magnetic field from the zero-field impedance by a scaling procedure originally proposed by Chambers. It is shown that the approximation of a local current-field relation ignores the Doppler effect on the carriers. When the proper nonlocal current-field relation is used, the theoretically predicted surface impedance is altered substantially in the vicinity of the resonance. The nonlocal effects can, in fact, be qualitatively reproduced by using a local theory and replacing $\ensuremath{\omega}$ by ${\ensuremath{\omega}}_{\mathrm{eff}}=\ensuremath{\omega}\ifmmode\pm\else\textpm\fi{}\frac{{v}_{F}}{{\ensuremath{\delta}}_{i}}$, where ${\ensuremath{\delta}}_{i}$ is the inductive skin depth. The nonlocal theory leads to: (a) a resonance in the resistance at the Doppler shifted frequency $\ensuremath{\omega}=|{\ensuremath{\omega}}_{c}|\ensuremath{-}\frac{{v}_{F}}{{\ensuremath{\delta}}_{i}}$; (b) a shift in the threshold field required for the onset of an undamped electromagnetic wave (helicon wave). Recent experiments on Bismuth by Kirsch and Redfield show structure believed to correspond to the Doppler shifted resonance discussed.