Brillouin-Zone—Fermi-Surface Interactions in Pure and Lead-Doped Indium
Abstract
Electrical resistivity anisotropies ($a\ensuremath{\equiv}\frac{{\ensuremath{\rho}}_{\ensuremath{\perp}}}{{\ensuremath{\rho}}_{\ensuremath{\parallel}}}$, direction referred to the $c$ axis) of pure indium containing 0-9-at.% lead have been measured at 4.2, 77, and 273 \ifmmode^\circ\else\textdegree\fi{}K. For pure indium it was found that $a(77)=0.988\ifmmode\pm\else\textpm\fi{}0.003$, while $a(273)=1.037\ifmmode\pm\else\textpm\fi{}0.003$; thus the direction of maximum resistivity changes from the $c$ to the $a$ direction as the temperature goes from 77 to 273 \ifmmode^\circ\else\textdegree\fi{}K. This behavior is interpreted in terms of the resistivity anisotropy model of Klemens, Van Baarle, and Gorter, which is also used to qualitatively explain the observed anisotropies of the indium-lead alloys studied. Anomalies in the resistivity anisotropy were observed at 3.5- and 7.0 at.% lead, which were traced to anomalous behavior in the resistivity perpendicular to the $c$ axis. The behavior at 7.0-at.% lead is interpreted as the Fermi surface popping through the (200) zone boundary. The temperature-dependent resistivity anisotropies of indium-lead alloys at 77 and 273 \ifmmode^\circ\else\textdegree\fi{}K were determined, and at 273 \ifmmode^\circ\else\textdegree\fi{}K, the direction of maximum temperature-dependent resistivity was found to change from the $a$ to the $c$ direction between 6- and 7-at.% lead. This behavior is attributed to an increasing perturbation of the indium lattice periodic potential by the lead ions at the relatively high temperature of 273 \ifmmode^\circ\else\textdegree\fi{}K, and it is interpreted in terms of a breakdown in the $\ensuremath{\delta}$-function potential approximation in the model of Klemens et al.