Lattice Thermal Conductivity, Nernst-Ettinghausen Effect, and Specific Heat in Antimony at Low Temperature

Abstract

The lattice thermal conductivity, the high-field Nernst-Ettinghausen thermoelectric coefficient, and the specific heat of antimony have been determined in the temperature range 0.4-2.4\ifmmode^\circ\else\textdegree\fi{}K. Thermal-conductivity results confirm the predominance of phonon-electron normal scattering in the lowest range of temperatures with the expected ${T}^{2}$ law. The dramatic increase in the lattice thermal conductivity above 1.5\ifmmode^\circ\else\textdegree\fi{}K is thought to be due to the inability of the electrons to scatter phonons with wave numbers $q>2{k}_{F}$, where $2{k}_{F}$ is the diameter of a charge carrier's Fermi pocket. An effective scattering Debye temperature of ${\ensuremath{\Theta}}^{*}=(\frac{2{k}_{F}}{{q}_{D}})\ensuremath{\Theta}\ensuremath{\approx}25\ifmmode^\circ\else\textdegree\fi{}$K is in good agreement with experimental results. Nernst-Ettinghausen results give the total electronic density of states $Z=(1.10\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{33}$ ${\mathrm{erg}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}3}$; the presence of a phonon-drag contribution is confirmed and discussed. The specific-heat results, $C=(116.5\ifmmode\pm\else\textpm\fi{}6.4)T+(211.0\ifmmode\pm\else\textpm\fi{}5.3){T}^{3}+1.97\ifmmode\pm\else\textpm\fi{}0.23){T}^{\ensuremath{-}2}$ in \ensuremath{\mu}J ${(\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\phantom{\rule{0ex}{0ex}}\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{K})}^{\ensuremath{-}1}$, are compared with the results of transport measurements and with recent specific-heat determinations.