Hidden in plain heat: anomalous Lorenz number in the thermoelectric alloy Bi_0.4Sb_1.6Te₃.

Abstract

Ternary and quaternary alloys based on Bi₂Te₃ remain to date the most efficient materials for thermoelectric cooling around room temperature. Among the various strategies developed over the last decades to further enhance their performance, nanostructuration induced by melt-spinning has proven to be effective, yielding higher values of the dimensionless thermoelectric figure of merit, attributed primarily to a significant decrease in the lattice thermal conductivity <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>L</mi></mrow> </msub> </math> . Here, we present measurements of the total thermal conductivity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi></math> of two polycrystalline samples of the alloy Bi_0.4Sb_1.6Te₃ prepared by conventional powder metallurgy and melt-spinning at low temperatures and under high magnetic fields of up to 14 T that challenge this view. By directly accessing <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>L</mi></mrow> </msub> </math> without relying on the Wiedemann-Franz law, we show that both samples exhibit a similar <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>L</mi></mrow> </msub> <mrow><mo>(</mo> <mrow><mi>T</mi></mrow> <mo>)</mo></mrow> </math> dependence below ∼70 K. The difference with the <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>L</mi></mrow> </msub> <mrow><mo>(</mo> <mrow><mi>T</mi></mrow> <mo>)</mo></mrow> </math> dependences predicted by this simple law is tied to anomalously low Lorenz number <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> , the values and temperature dependence of which are shaped by inelastic scattering processes that relax charge and energy flows in an inequivalent manner. Not captured by conventional transport models, the finite-temperature, downward deviations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi> <mrow><mo>(</mo> <mrow><mi>T</mi></mrow> <mo>)</mo></mrow> </math> are successfully reproduced by a theoretical model that includes inelastic electron-electron and electron-optical phonon scattering. These findings show that the melt-spinning-induced nanostructuration has a weaker influence on <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>κ</mi></mrow> <mrow><mi>L</mi></mrow> </msub> </math> than previously thought, and pave the way to a better understanding of the deviations from the Wiedemann-Franz law reported in a growing number of complex thermoelectric materials.