Thermoelectric Properties of Type-I and Type-II Nodal Line Semimetals: A Comparative Study

We investigate the thermoelectric (TE) properties of nodal line semimetals (NLSs) using a combination of semi-analytical calculations within Boltzmann's linear transport theory and the relaxation time approximation, along with first-principles calculations for the so-called type-I and type-II NLSs. We consider the conduction and valence bands that cross near the Fermi level of these materials through first-principles calculations of typical type-I (TiS) and type-II (Mg$_3$Bi$_2$) NLSs and use the two-band model fit to find the Fermi velocity $v_{F}$ and effective mass $m$ that will be employed as the initial energy dispersion parameters. The optimum curvature value for each energy band is searched by tuning both $v_{F}$ and $m$ to improve the TE properties of the NLSs. By systematically comparing all of our calculation results, we observe that tuning $v_{F}$ significantly improves TE properties in both types of NLS compared to tuning $m$. We also find that in all TE metrics, the type-I NLS surprisingly can surpass the type-II NLS, which seems counter-intuitive to the fact that within the two-band model, the type-I NLS contains a parabolic band while the type-II NLS possesses a higher-order, Mexican-hat band. Our study demonstrates that optimizing the curvature of energy bands by tuning $v_F$ can significantly improve the TE performance of NLSs. This approach could guide future efforts in exploring other semimetals as potential TE materials by manipulating their band structures.