Effect of copper doping on kinetic coefficients and their anisotropy in PbSb$_2$Te$_4$

In anisotropic PbSb$_2$Te$_4$ and PbSb$_2$Te$_4$:Cu single crystals, nine main independent components of the Hall, electrical-conductivity, thermopower, and Nernst-Ettingshausen effects and their anisotropy in the range 77–450 K have been studied. PbSb$_2$Te$_4$ single crystals exhibit a high hole concentration ($p\approx$ 3 $\times$ 10$^{20}$ cm$^{-3}$). Copper exhibits a donor effect and significantly (approximately by a factor of 2) reduces the hole concentration in PbSb$_2$Te$_4$. The temperature dependences of the kinetic coefficients, except for the Hall effect, have a form typical of the one-band model. The significant anisotropy of the Hall coefficient $R_{123}/R_{321}\approx$ 2 at low temperatures corresponds to the multi-ellipsoid model of the energy spectrum of holes in PbSb$_2$Te$_4$. An important feature of the data on transport phenomena is the high thermopower anisotropy ($\Delta S\approx$ 60–75 $\mu$V/K) in the mixed conductivity region caused by the mixed scattering mechanism. Data on the anisotropy of the transverse Nernst–Ettingshausen effect confirm the mixed mechanism of hole scattering; in the cleavage plane, scattering at acoustic phonons dominates, while in the trigonal axis direction, impurity scattering appears significant. Doping with copper enhances the role of impurity scattering in the direction of the trigonal axis $c_3$; as a result, two components of the Nernst–Ettingshausen tensor $Q_{321}$ and $Q_{132}$ in the PbSb$_2$Te$_4$:Cu single crystal are positive at low temperatures, whereas, in the undoped crystal, only the $Q_{321}$ component is positive.