Low-Dimensional Transport and Large Thermoelectric Power Factors in Bulk Semiconductors by Band Engineering of Highly Directional Electronic States

Thermoelectrics are promising for addressing energy issues but their exploitation is still hampered by low efficiencies. So far, much improvement has been achieved by reducing the thermal conductivity but less by maximizing the power factor. The latter imposes apparently conflicting requirements on the band structure: a narrow energy distribution and a low effective mass. Quantum confinement in nanostructures and the introduction of resonant states were suggested as possible solutions to this paradox, but with limited success. Here, we propose an original approach to fulfill both requirements in bulk semiconductors. It exploits the highly directional character of some orbitals to engineer the band structure and produce a type of low-dimensional transport similar to that targeted in nanostructures, while retaining isotropic properties. Using first-principle calculations, the theoretical concept is demonstrated in ${\mathrm{Fe}}_{2}YZ$ Heusler compounds, yielding power factors 4 to 5 times larger than in classical thermoelectrics at room temperature. Our findings are totally generic and rationalize the search of alternative compounds with similar behavior. Beyond thermoelectricity, these might be relevant also in the context of electronic, superconducting, or photovoltaic applications.

Figure 1

Electronic band structures and power factors ($\mathrm{PF}=S^2\sigma$) at 300 K for the sets S1 and S2 of compounds. ${\mathrm{Fe}}_{2}YZ$ full Heusler compounds with $Y=\mathrm{V}$ (green lines), Nb (blue lines), Ta (magenta lines) and $Z=\mathrm{Al}$, Ga, In in the first row. ${\mathrm{Fe}}_{2}YZ$ full Heusler compounds with $Y=\mathrm{Ti}$ (green lines), Zr (blue lines), Hf (magenta lines) and $Z=\mathrm{Sn}$, Ge, Si in the second row. Dotted lines indicate the highly dispersive lowest conduction band of dominant $Y$ $e_g$ character. The bold lines show the band of Fe $e_g$ character that is flat along the $\mathrm{\Gamma }X$ direction and highly dispersive along others.

Figure 2

Atomic structure, Fermi surfaces, and thermodynamical stability of ${\mathrm{Fe}}_{2}YZ$ compounds. (a) Full Heusler structure consisting of four interpenetrating fcc lattices with Fe, $Y$, and $Z$ atoms represented in red, green and blue. It can also be viewed as alternating ${\mathrm{Fe}}_2$ and $YZ$ planes along the $\{001\}$ (see ${\mathrm{Fe}}_2$ planes highlighted in grey), $\{100\}$, and $\{010\}$ directions. (b) Sketch of the Fe $d_{x^2-y^2}$ $e_g$ orbitals overlapping in $\{001\}\text{−}{\mathrm{Fe}}_2$ planes. (c,d) Fermi surfaces of ${\mathrm{Fe}}_2\mathrm{VAl}$ and ${\mathrm{Fe}}_2\mathrm{TiSn}$ at doping concentration yielding the maximum PFs at 300 K. (e) Map of the thermodynamical stability (as measured by the energy with respect to hull) computed at 0 K as a function of the $Y$ and $Z$ atomic radii. A negative number (inverse energy above hull, green color) corresponds to a stable phase and a positive number (energy above hull, red color) to an unstable one. Circles (resp. squares) correspond to compounds (resp. not) previously synthesized.