Magnetothermoelectric effects in graphene and their dependence on scatterer concentration, magnetic field and band gap

TL;DR

This paper develops an analytical model for graphene's thermoelectric and electric transport properties considering various scatterers, magnetic fields, and band gaps, aligning well with experimental data and offering a more efficient alternative to Green's function methods.

Contribution

It introduces a semiclassical Boltzmann transport equation approach to analytically evaluate graphene's thermoelectric coefficients under diverse conditions, improving accuracy and computational efficiency.

Findings

Seebeck coefficient is odd function of Fermi energy.

Nernst coefficient is even function of Fermi energy.

Peaks increase with decreasing scatterer concentration and increasing temperature.

Abstract

Using a semiclassical Boltzmann transport equation (BTE) approach, we derive analytical expressions for electric and thermoelectric transport coefficients of graphene in the presence and absence of a magnetic field. Scattering due to acoustic phonons, charged impurities and vacancies are considered in the model. Seebeck ($S_{xx}$) and Nernst ($N$) coefficients have been evaluated as functions of carrier density, temperature, scatterer concentration, magnetic field and induced band gap, and the results are compared with experimental data. $S_{xx}$ is an odd function of Fermi energy while $N$ is an even function, as observed in experiments. The peaks of both coefficients are found to increase with decreasing scatterer concentration and increasing temperature. Furthermore, opening a band gap decreases $N$ but increases $S_{xx}$. Applying a magnetic field introduces an asymmetry in the variation of $S_{xx}$ with Fermi energy across the Dirac point. The formalism is more accurate and computationally efficient than the conventional Green's function approach used to model transport coefficients and can be used to explore transport properties of other exotic materials.