Multi-band analysis of temperature-dependent transport coefficients (conductivity, Hall, Seebeck, and Nernst) of Ni-doped CoSb3

Abstract

The experimental data on the temperature dependence of the four transport coefficients, i.e., the electrical conductivity (σ), Hall coefficient (RH), Seebeck coefficient (S), and Nernst coefficient (Q), of n-type Co0.999Ni0.001Sb3 reported by Sun et al. [Nat. Commun. 6, 7475 (2015)] have been analyzed in a multi-band model, especially focusing on the low temperature data. The multi-band model includes not only the lowest valley of the conduction band at the Γ point but also satellite valleys at the second minima together with an impurity band. The lowest valley at the Γ point is assumed to split into the c1 band and the spin-orbit split-off (so) band. For the analysis, the general expression of the Nernst coefficient in the multi-band model is derived. At such low temperatures that the other bands than the c1 and the impurity band can be neglected, this expression is shown to be approximated as the sum of three terms: the intrinsic terms due to the Nernst coefficients in the two bands themselves and a cross term proportional to the difference of Seebeck coefficients between the two bands. As a result of the analysis, it is proved that the anomalous positive peak of S(T) observed around T = 20 K as well as the sharp rise of the Hall mobility observed from 15 K to 40 K are due to the transition from hopping conduction in the impurity band to conduction in the c1 band. On the other hand, the pronounced peak of Q(T) observed slightly below 40 K is proved to be due to the cross term between the impurity band and the c1 band. In addition, a shoulder of Q(T) appeared around T = 80 K lends clear evidence of the existence of the so band, while the increase in both of σ(T) and |S(T)| above 150 K suggests the existence of the satellite valleys.