The Shanghai Institute of Ceramics has made significant progress in the study of critical thermoelectric performance

Critical phenomena are extremely common in nature. When materials undergo critical transitions, they exhibit pronounced atomic dynamic disorder and critical fluctuations, leading to anomalous physical properties. In earlier studies, the Shanghai Institute of Ceramics, Chinese Academy of Sciences, discovered that both the resistivity ρ and the Seebeck coefficient α sharply increase during the dynamic phase transition of materials, resulting in exceptionally high thermoelectric figure-of-merit (Adv. Mater. 2013). Based on a correction to the classical heat-transport equation, the study elucidated the impact of heat absorption and release during phase transitions on thermal-flow transport (Adv. Mater. 2019). The combination of thermoelectric effects and critical phenomena has given rise to the emerging field of critical electrothermal transport research. However, current understanding of the underlying physical mechanisms mostly remains at a qualitative level, or focuses solely on quantitative physical models for either resistivity or the Seebeck coefficient alone. Therefore, a deeper comprehension and characterization of critical electrothermal transport phenomena, along with the development of a universal model that encompasses all aspects of electrical transport, would hold significant theoretical importance and practical value for advancing research into critical thermoelectric effects.

Recently, Researcher Shi Xun and Researcher Chen Lidong from the Shanghai Institute of Ceramics, in collaboration with Associate Professor Zhao Kunpeng from Shanghai Jiao Tong University and Professor Chen Hongyi from Central South University, established a quantitative model for critical electrotransport properties based on Landau theory. This model reveals the mechanisms by which band broadening and phonon soft-mode effects during dynamic phase transitions influence electrotransport performance, enabling controllable regulation of order parameters, phase-transition temperatures, and critical thermoelectric properties. During second-order phase transitions, parameters such as atomic structure, chemical composition, and density exhibit critical fluctuations that significantly affect the electronic band structure, phonon spectra, and electron-phonon coupling. The dynamic disorder and critical fluctuations of atoms give rise to two important physical effects: broadening of the band-edge state density and softening of transverse acoustic phonons (see Figure 1). Based on classical Landau theory, quantitative expressions for the Seebeck coefficient and resistivity under the influences of band broadening and phonon soft modes were derived. By introducing the phase-transition parameter b, a relationship between the Seebeck coefficient and resistivity during critical phase transitions was established. The study found that the band-broadening effect during critical phase transitions can significantly enhance the material's Seebeck coefficient without substantially affecting its resistivity; the strong coupling between softened phonons and electrons not only increases the Seebeck coefficient but also elevates the resistivity. As the value of the phase-transition parameter b decreases, structural fluctuations during the phase transition become more pronounced. The band-broadening effect causes changes in the distribution of charge carriers across different energy levels, thereby increasing the entropy carried by these carriers and leading to an increase in the Seebeck coefficient. A smaller b value reduces the frequency of transverse optical phonons, intensifying the electron-phonon coupling and resulting in increased resistivity. At the same time, the rise in carrier transport entropy further boosts the Seebeck coefficient (see Figure 1).

First-principles calculations and experimental studies have verified the universality and effectiveness of this model. The research team used first-principles methods to calculate the band structure of Cu2Se under different order parameters and found that structural fluctuations during the phase transition hardly alter the shape of the band, yet a noticeable broadening effect appears at the band edges. This finding is consistent with the observed trends in electrical properties, and the broadening energy ΔE also exhibits a λ-shaped profile. Based on a modified conductivity-Seebeck coefficient measurement system, the research team precisely measured the electrical conductivity and Seebeck coefficient of the Cu2Se1-xSx solid solution (x = 0, 0.04, 0.08, 0.12) during the critical phase transition process. The experimental results show that both the Seebeck coefficient and resistivity of Cu2Se1-xSx significantly increase during the phase transition, which is consistent with the theoretical predictions. As the S solute content increases, the phase-transition parameter b gradually rises, causing the ratio Δαmax/α0 between the phase-transition Seebeck coefficient and the Seebeck coefficient of the normal phase to decrease, while the ratio Δρmax/ρ0 of resistivity remains essentially unchanged—both findings are in good agreement with the model predictions (see Figure 2). Moreover, S solute incorporation effectively lowers the phase-transition temperature, narrows the phase-transition range, and reduces the phase-transition enthalpy. During the critical phase transition, the thermal conductivity of Cu2Se1-xSx drops dramatically, leading to a significant enhancement in thermoelectric performance. At the critical temperature, the figure of merit zT for thermoelectric performance reaches 1.3, which is 2.5 times higher than that of the normal static phase at the same temperature (see Figure 3). The device performance of thermoelectric single-couple cooling modules also shows a substantial improvement within the phase-transition range, following the same trend as the material's thermoelectric performance. This research not only provides a new theoretical framework for studying critical electrical transport properties during dynamic phase transitions but also points to new directions for the control and optimization of critical thermoelectric effects.

The relevant research findings, titled “Modeling Critical Thermoelectric Transports Driven by Band Broadening and Phonon Softening,” have been published in Nature Communications (2024, doi:10.1038/s41467-024-45093-6). Zhao Kunpeng and Yue Zhongmou, a doctoral graduate from the Shanghai Institute of Ceramics, are co-first authors of the paper. This research was supported by funding from projects including the National Natural Science Foundation of China and the Shanghai Municipal Basic Research Special Zone Program.

Paper link: https://www.nature.com/articles/s41467-024-45093-6

Figure 1: Band broadening and phonon soft-mode effect during the critical phase transition. (a) Schematic illustration of structural fluctuations during the phase transition, (b) Free energy Φ and order parameter ξ for the critical phase transition, (c) Schematic illustration of the band broadening effect, (d) Schematic illustration of phonon softening, (e) Relationship between the increase in the Seebeck coefficient and temperature T and the phase-transition parameter b during the critical phase transition, (f) Relationship between the increase in resistivity and temperature T and the phase-transition parameter b during the critical phase transition.

Figure 2. Critical electrical transport properties of the Cu2Se1-xSx solid-solution alloy. (a) Variation of the phase transition temperature and phase transition parameter with solid-solution content x; (b) Variation of resistivity with temperature; (c) Variation of the Seebeck coefficient with temperature; (d) Variation of the ratio Δαmax/α0 between the phase-transition Seebeck coefficient and the normal-phase Seebeck coefficient, as well as the ratio Δρmax/ρ0 between the change in resistivity and the initial resistivity, with the phase-transition parameter b; (e) Increase in resistivity caused by the coupling between soft phonons and charge carriers; (f) Increase in the Seebeck coefficient due to band broadening, as well as the additional increase in the Seebeck coefficient resulting from the coupling between soft phonons and charge carriers.

Figure 3. Thermal conductivity and figure of merit for thermoelectric performance during the critical phase transition. (a) Thermal conductivity as a function of temperature; (b) Figure of merit zT as a function of temperature; (c) Average zT value from room temperature to the critical temperature; (d) Cooling temperature difference of the thermoelectric couple.