Nonlocal Effects in Low-Field Helicon Propagation in PbTe

Abstract

Helicon propagation has been studied in the region of low magnetic fields, where band structure and nonlocal Landau damping effects produce sizable corrections to the high-field dispersion relation. Good agreement with both the phase and amplitude of 9-GHz helicons in $n\ensuremath{-}\mathrm{P}\mathrm{b}\mathrm{T}\mathrm{e}$ at 4.2\ifmmode^\circ\else\textdegree\fi{}K is obtained by a semiclassical treatment of a degenerate, many-valley, ellipsoidal model. The calculation is carried out by expanding the conductivity tensor in powers of $\frac{1}{{B}_{0}}$, treating $\frac{\ensuremath{\omega}}{{\ensuremath{\omega}}_{c}}$, $\frac{1}{{\ensuremath{\omega}}_{c}\ensuremath{\tau}}$, and $\frac{q{v}_{F}}{{\ensuremath{\omega}}_{c}}$ as small quantities, where ${B}_{0}$ is the static magnetic field, ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency, $\ensuremath{\tau}$ is the collision time, $q$ is the wave number, and ${v}_{F}$ is the Fermi velocity. Because of the anisotropic energy surfaces in PbTe, Landau damping occurs for propagation along the field as well as at an angle. The corrections to the phase are quite sensitive to the transverse effective mass; comparison with experiment yields a value of $0.020{m}_{0}$ for the band-edge transverse mass in PbTe. It is also found that both relaxation to the local equilibrium and anisotropic scattering are important effects, although only the former is included in the theoretical calculations.