First-priniciple based study of transport properties of non-trivial topological fermions of CoSi

Abstract

Recently, CoSi has been identified to have unconventional electronic topology due to lack of inversion center in its B20 cubic structure. The electronic topology has been reported to be present at three nodal points found in the band structure. Two of these nodal points are situated at the $\Gamma$ (G1 \& G2) and one at $R$ (R1) point. Based on this, we present a study where various transport coefficients are investigated by using \textit{first-principle} based DFT method for the temperature (T) range 40-300 K. For the chemical potential ($\mu$) corresponding to energies of these nodal points and at the Fermi level (E$_F$), 3D constant energy surfaces are constructed. They have shown that the number of states available at energies of these nodal points and the E$_F$ follows an increasing trend as R1 $>$ G2 $>$ E$_F$ $>$ G1 at T = 0 K. Similar increasing behavior seems to follow by other transport coefficients at different $\mu$ with T rise such as electrical conductivity($\sigma$)/relaxation time($\tau$) ratio and electronic thermal conductivity ($\kappa_e/\tau$ = $\kappa^0$). For example, at T = 100 K, $\sigma / \tau$ $\sim$ 0.13$\times$10$^{20}$ $\Omega^{-1} m^{-1} s^{-1}$ at G1 whereas its value reaches $ \sim$ 0.18$\times$10$^{20}$ $\Omega^{-1} m^{-1} s^{-1}$ at R1 nodal point. However, Seebeck coefficient ($S$) seems to follow the trend as G2 $>$ E$_F$ $>$ R1 $>$ G1 at any given T. The values of $S$ are obtained to be positive at the $\mu$ corresponding to the G2, R1 and E$_F$ (except G1) which is increasing with the rise in T. Also, the dominant charge carriers at G1 point are found to be electrons for T $<$ 225 K whereas for T $>$ 225 K, the charge carriers are obtained to be dominated by holes. Furthermore, the doping concentrations have also been calculated for G1, G2 and R1 points.