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We develop a new theoretical scheme for charge transport and thermoelectric response in two-dimensional disordered systems exhibiting crossover from weak localization (WL) to strong localization (SL). The scheme is based on the scaling theory for Anderson localization combined with the Kubo-Luttinger theory. Key aspects of the scheme include introducing a unified $\beta$ function that seamlessly connects the WL and SL regimes, as well as describing the temperature ($T$) dependence of the conductance from high to low $T$ regions on the basis of the dephasing length. We found that the Seebeck coefficient, $S$, behaves as $S\propto T$ in the WL limit and as $S\propto T^{1-p}$ ($p < 1$) in the SL limit, both with possible logarithmic corrections. The scheme is applied to analyze experimental data for thin films of the p-type organic semiconductor poly[2,5-bis(3-alkylthiophen-2-yl)thieno(3,2-b)thiophene] (PBTTT)., Comment: 6 pages, 2 figures

The development of good thermoelectric materials exhibiting high $ZT$ (=$\frac{PF}{\kappa} T$) requires maximizing power factor, $PF$, mainly governed by electrons, and minimizing thermal conductivity, $\kappa$, associated not only with electrons but also with phonons. In the present work, we focus on the GeTe and Mg$_3$Sb$_2$ as high $ZT$ materials with inhomogeneous structures and analyze both electrical conductivity, $L_{11}$, and Seebeck coefficient, $S$, with help of Sommerfeld-Bethe formula, resulting in understanding the temperature dependence of $PF$ and the identification of electrons contribution to thermal conductivity, $\kappa_{\rm el}$. Comparing the obtained $\kappa_{\rm el}$ and experimentally measured $\kappa$, the temperature dependence of phonons contribution to thermal conductivity, $\kappa_{\rm ph}=\kappa-\kappa_{\rm el}$, is inferred and analyzed based on the formula by Holland. Comparison of the GeTe and Mg$_3$Sb$_2$ with different types of crystal structures, i.e., GeTe being of a semiordered zigzag nanostructure like a disrupted herringbone structure while Mg$_3$Sb$_2$ of rather uniform amorphous structure, discloses that size effects on temperature dependence of $\kappa_{\rm ph}$ is large in the former, while very small in the latter. Hence, it is concluded that not only the size of the grain but also its shape has an important influence on $\kappa_{\rm ph}$ and then $ZT$.

We propose a simple theoretical model referred to as the {\it two-band model} to realize both a large Seebeck coefficient and high electrical conductivity, resulting in a high thermoelectric (TE) power factor ($PF$). Using the Kubo--Luttinger linear response theory, we apply this model to the TE response of an FeSe thin film reported by Shimizu {\it et al.} to show a high $PF$ with strong temperature dependence. The effects of superconducting fluctuations and excitonic correlations are found to not be critical.

We have theoretically investigated thermoelectric (TE) effects of narrow-gap single-walled carbon nanotubes (SWCNTs) with randomly substituted nitrogen (N) impurities, i.e., N-substituted (20,0) SWCNTs with a band gap of 0.497 eV. For such a narrow-gap system, the thermal excitation from the valence band to the conduction band contributes to its TE properties even at the room temperature. In this study, the N-impurity bands are treated with both conduction and valence bands taken into account self-consistently. We found the optimal N concentration per unit cell, $c_{\rm opt}$, which gives the maximum power factor ($PF$) for various temperatures, e.g., $PF=$0.30$\rm{W/K^2m}$ with $c_{\rm opt}=3.1\times 10^{-5}$ at 300K. In addition, the electronic thermal conductivity has been estimated, which turn out to be much smaller than the phonon thermal conductivity, leading to the figure of merit as $ZT\sim 0.1$ for N-substituted (20,0) SWCNTs with $c_{\rm opt}=3.1\times 10^{-5}$ at 300K.