First-principles-aided evaluation of the Nernst coefficient beyond the constant relaxation time approximation

Abstract

The solution of the Boltzmann Transport Equation (BTE) under open voltage conditions and in the presence of simultaneously applied magnetic field and temperature gradient results in the so-called Nernst response of the electrons. The calculation of the Nernst coefficient using first-principles calculations as an extension of the BoltzWann code and under Jones–Zener expansion valid for weak magnetic fields has been the subject of our previous work which provided a general framework for the calculation of the Nernst effect but was not able to capture the experimental results due to the constant relaxation time approximation used. In Contrast to the Seebeck coefficient which is not sensitive to the details of the relaxation times, the Nernst coefficient is proportional to the carrier mobility and hence is greatly affected by the relaxation times. In this work, we focus on the inclusion of the energy-dependent electron–phonon and the electron–impurity relaxation times in our formalism. Using the developed formalism, we successfully reproduced the experimental data of several samples. In this paper, we report our results on Ge, Si, and InSb samples. However, the code is not limited to the reported samples and supports a wide range of materials.