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GeTe, as a p-type semiconductor, has been intensively studied in recent years as a promising lead-free midtemperature-range thermoelectric (TE) material. Herein, we report an improved energy conversion efficiency (η) using a two-step TE properties optimization in Mn−Sb co-doped GeTe by engineering electronic structure and lattice dynamics. Mn−Sb co-doping enhances the TE properties of GeTe, as evidenced from both experiments and first-principles-based theoretical calculations. The density functional theory (DFT) calculations indicate that Mn−Sb co-doping improves the band convergence and optimizes the Fermi level position. This in turn helps in enhancing the Seebeck coefficient (α). As a result of the optimized Seebeck coefficient and electrical conductivity (σ), an enhanced power factor (α 2 σ) is obtained for the Mn−Sb co-doped system. Moreover, a significant reduction in the phonon (lattice) thermal conductivity (κ ph ∼ 0.753 W/mK) at 748 K is observed for Ge 0.87 Mn 0.05 Sb 0.08 Te, attributed to the point-defect scattering and reduced phonon group velocity. The synergistic improvement in α and reduction in κ ph result in a maximum figure-of-merit (zT) of 1.67 at 773 K, with an average zT (zT av ) of ∼ 0.9 for Ge 0.87 Mn 0.05 Sb 0.08 Te over a temperature range of 300−773 K, leading to an η of ∼12.7%.

Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of β-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of β-galactosidase.

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