Enhanced thermoelectric performance by van Hove singularities in the density of states of type-II nodal-line semimetals

The effects of the unique density of states (DOS) of a topological type-II\nnodal-line semimetal (NLS) on its thermoelectric (TE) transport properties are\ninvestigated through a combination of semi-analytical and first-principles\nmethods with "spinless Mg$_3$Bi$_2$" as artificial material. The DOS in such a\ntype-II NLS possesses two van Hove singularities near the energy of the nodal\nline that leads to a large $S$ value compared to the normal metals. Combined\nwith the linear band at the nodal line that gives high electrical conductivity\n$\\sigma$, the type-II NLS can exhibit a relatively high TE power factor\n($\\text{PF}=S^2\\sigma$) at the nodal line. In particular, we find $\\text{PF}\n\\sim 60$ $\\mu$W/cmK$^2$ at 300 K for the n-type Mg$_3$Bi$_2$ by considering the\nelectron-phonon scattering, in which the relaxation time $\\tau$ of carriers can\nbe expressed as $\\tau\\propto\\text{DOS}^{-1}$ for the type-II NLS. Furthermore,\nwe optimize parameters for the TE power factor of type-II NLSs in general by\nadopting the two-band model with the DOS-dependent relaxation time\napproximation. Our results suggest the type-II NLSs as a potential class of\nhigh-performance TE materials among metals and semimetals, which are\ntraditionally considered not good TE materials compared to semiconductors.\n