Dimensional transport crossovers in thermoelectrics revealed by a simple transport model

Quantum confinement gives low-dimensional materials distinctive electronic behaviour, but assessing their effective band structure dimensionality (D) is difficult. Conventional probes such as angle-resolved photoemission spectroscopy (ARPES) or scanning tunneling microscopy (STM) demand ultra clean surfaces and expensive facilities. We introduce a generalized transport model that functions as an internal dimensionality meter: by tracking how the Seebeck coefficient varies with carrier concentration or temperature, we deduce D from two scaling laws, $$S\propto \left(\frac{D}{2}\right){{\mathrm{ln}}}T$$ in non-degenerate regimes (e.g. $$\left|S\right|\ge 200{{{\rm{\mu }}}}{{{\rm{V}}}}{{{{\rm{K}}}}}^{-1}$$ ) and $$S\propto {n}^{-2/D}$$ in degenerate regimes (e.g. $$\left|S\right|\le 150\,{{{\rm{\mu }}}}{{{\rm{V}}}}{{{{\rm{K}}}}}^{-1}$$ ). Applying this approach to SrTiO3, few-layer Bi2O2Se and Pb1-xSnxTe uncovers temperature-, doping- and alloy-induced crossovers between three-dimensional and lower-dimensional transport. The method offers a rapid, scattering independent framework to design quantum and thermoelectric properties. A simple transport model infers a material’s electronic dimensionality from standard transport measurements, revealing temperature-, doping- and alloying-driven shifts between low-dimensional and 3D transport in SrTiO3, Bi2O2Se and Pb1-xSnxTe.