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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.

The present study has been carried out to understand the effect of electronic correlations on the recently found fermions in CoSi. For which the spectral functions of bulk and (001) surface of CoSi have been investigated by using DFT+DMFT advanced methodology at T = 100 K with and without inclusion of spin-orbit coupling (SOC). All the newly found fermions are observed at $\Gamma$ and $R$ points similar to other theoretical and experimental reports. Our DFT+DMFT calculations for the bulk states have shown one extra hole pocket at $M$ point. Both coherent and incoherent features have been observed in the spectra of bulk CoSi. This indicates the presence of quasiparticle-quasiparticle (QP-QP) interactions which is eventually affecting the lifetime ($\tau$) of exotic fermionic QPs. For instance, the calculated $\tau$ for QPs at $\omega \sim $ -30 and -186 mev are found to be $\sim 10^{-9}$ s and $\sim 10^{-12}$ s, respectively when SOC is not considered. However, $G_0W_0$ corrections have shown $\tau$ for spin-1 fermionic QP at $\Gamma$ to be infinite while for double Weyl fermionic QP at $R$ point to be $\sim 10^{-12}$ s. Their effective masses ($m^*$) have also been calculated as $\sim$ 1.60 and 1.64 at $\Gamma$ and $R$ points, respectively. Furthermore, the spectral functions at T = 100 K of (001) surface have also shown both coherent and incoherent features. Consequently, at $\omega$ = 0 for surface states $\tau$ has been calculated of the order $\sim 10^{-8}$s for both without SOC and with SOC inclusions.

Electronic structures of FeSi and Fe$_{1.02}$Si$_{0.98}$ under pressure (achieved through volume compression) have been investigated by using DFT+DMFT and KKR-CPA methods, respectively. The widening of band-gap with increasing pressure suggests that the experimentally observed insulator to metal transition temperature should shift towards the higher temperature for FeSi. KKR-CPA calculations have shown the presence of impurity states in the gapped region which predicts the half-metallic nature. The closure of gap (in one spin channel) with pressure increment appears to be responsible for experimentally observed semiconductor to metal transition in Fe excess samples at a temperature below 50 K. Magnetic moments at Fe excess sites are found to be decreasing with increasing pressure from 2.4 $\mu_B$ per Fe atom (612 Bohr$^3$) to 1.2 $\mu_B$ per Fe atom (507 Bohr$^3$). Moreover, for FeSi the calculated local spin susceptibility has shown decreasing behavior with pressure rise similar to experimental result.

We have investigated electronic energy band structures and partial density of states of intermetallic compounds $\textit{viz.}$ CrSi, MnSi, FeSi and CoSi, by using density functional theory (DFT). CrSi \& MnSi, FeSi and CoSi have metallic, indirect band gap semiconducting (band gap $ \sim$ 90 meV) and semi-metallic ground state, respectively. On studying the band structures while going across the series Cr-Co, the occupied bands around the Fermi level are getting narrower while the unoccupied bands are getting wider. Similarly, band edge in partial density of states is shifting away from the Fermi level due to increased hybridizations. The effective mass of holes for FeSi is found to be much larger than that of electrons, giving rise to positive Seebeck coefficient and negative Hall coefficient, which is consistent with experimental results. For different ionic states of 3\textit{d}-metal, the values of $\textit{$U_{eff}$}$ and $\textit{J}$ are evaluated by using constrained DFT method. $\textit{$U_{eff}$}$ ($\textit{J}$) for $2^{+} $ ionic state across the series are $\sim $ 3.3 eV ($\sim $0.65 eV), $\sim $ 3.7 eV ($\sim $0.72 eV), $\sim $ 4.4 eV ($\sim $ 0.82 eV) and $\sim $ 4.5 eV ($\sim $ 0.87 eV). $\lambda$ and $\textit{J}$ are also calculated by considering Yukawa form of Coulomb interaction. $\lambda $ values for $2^{+} $ ionic state along the series are $\sim $ 1.97 a.$u^{-1}$, $\sim $ 2.07 a.$u^{-1}$, $\sim $ 2.07 a.$u^{-1}$ and $\sim $ 2.34 a.$u^{-1}$. 4$\textit{s}$ electrons are found to be contributing more in screening the 3$\textit{d}$ electrons as compared to 4$\textit{p}$ electrons of 3$\textit{d}$ metals., Comment: 2 figures and 4 tables

In this work, we present a systematic study of the occupied and unoccupied electronic states of LaCoO$_{3}$ compound using DFT, DFT+$\textit{U}$ and DFT+embedded DMFT methods. The value of $\textit{U}$ used here is evaluated by using constrained DFT method and found to be $ \backsim $ 6.9 eV. It is found that DFT result has limitations with energy positions of PDOS peaks due to its inability of creating a hard gap although the DOS distribution appears to be fine with experimental attributes. The calculated value of $\textit{U}$ is not an appropriate value for carrying out DFT+$\textit{U}$ calculations as it has created an insulating gap of $ \backsim $ 1.8 eV with limitations in redistribution of DOS which is inconsistent with experimental spectral behaviour for the occupied states mainly. However, this value of $\textit{U}$ is found to be an appropriate one for DFT+embedded DMFT method which creates a gap of $\backsim $ 1.1 eV. The calculated PDOS of Co 3$\textit{d}$, La 5$\textit{d}$, La 4$\textit{f}$ and O 2$\textit{p}$ states are giving a remarkably good explanation for the occupied and unoccupied states of the experimental spectra in the energy range $\backsim $ -9.0 eV to $\backsim $ 12.0 eV.