Skin-Deep Aspect of Thermopower in Bi₂Q₃, PbQ, and BiCuQO (Q = Se, Te): Hidden One-Dimensional Character of Their Band Edges Leading to High Thermopower

ConspectusThermoelectric (TE) materials have received much attention because of their ability to convert heat energy to electrical energy. At a given temperature T, the efficiency of a TE material for this energy conversion is measured by the figure of merit zT, which is related to the thermopower (or Seebeck coefficient) S, the thermal conductivity κ, and the electrical conductivity σ of the TE material as zT = (S2σT)/κ. Bi2Q3 and PbQ (Q = Se, Te) are efficient TE materials with high zT, although they are not ecofriendly and their stability is poor at high temperature. In principle, a TE material can have a high zT if it has a low thermal conductivity and a high electrical conductivity, but the latter condition is hardly met in a real material because the parameters S, σ and κ have a conflicting dependence on material properties. The difficulty in searching for TE materials of high zT is even more exasperated because the relationship between the thermopower S and the carrier density n (hereafter, the S-vs-n relationship) for the well-known hole-doped samples of BiCuSeO showed that the hole carriers responsible for their thermopower are associated largely with the electronic states lying within ∼0.5 eV of its valence band maximum (VBM). Thus, the states governing the TE properties lie in the "skin-deep" region from the VBM. For electron-doped TE systems, the electron carriers responsible for their thermopower should also be associated with the electronic states lying within ∼0.5 eV of the conduction band minimum (CBM). This makes it difficult to predict TE materials of high zT. One faces a similar skin-deep phenomenon in searching for superconductors of high transition temperature because the transition from a normal metallic to a superconducting state involves the normal metallic states in the vicinity of the Fermi level EF. Other skin-deep phenomena in metallic compounds include the formation of charge density wave (CDW), which involves the electronic states in the vicinity of their Fermi levels. For magnetic materials of transition-metal ions, the preferred orientation of their spin moments is a skin-deep phenomenon because it is governed by the interaction between the highest-occupied and the lowest unoccupied d-states of these ions. In the present work we probe the issues concerning how to find the possible range of thermopower expected for a given TE material and hence how to recognize what experimental values of thermopower are expected or unusual. For these purposes, we analyze the accumulated S and n data on the three well-studied TE materials, Bi2Q3, PbQ, and BiCuQO (Q = Se, Te), as representative examples, in terms of the ideal theoretical S-vs-n relationships, which we determine for their defect-free Bi2Q3, PbQ, and BiCuQO structures using density functional theory (DFT) calculations under the rigid band approximation. We find that the general trends in the experimental S-vs-n relationships are reasonably well explained by the calculated S-vs-n relationships, and the carrier densities covering these relationships are associated with the states lying within ∼0.5 eV from their band edges confirming the skin-deep nature of their thermoelectric properties. Despite the fact that these TE materials are not one-dimensional (1D) in structure, they mostly possess sharp density-of-state peaks around their band edges because their band dispersions have a hidden 1D character so their thermopower is generally high in magnitude.