Electronic correlation effect on nontrivial topological fermions in CoSi

Abstract

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 using DFT + DMFT advanced methodology at T = 100 K with and without inclusion of spin–orbit coupling (SOC). The Co ${d_{xz}}$ + ${d_{yz}}$ and $d_{z^2}$ bands seem to contribute at threefold degenerate $\Gamma$ point. On the other hand, fourfold degenerate R point seems to posses maximum of Co $d_{x^2-y^2} + d_{xy}$ orbitals and minimum of $d_{xz} + d_{yz}$ orbitals. However, SOC and electronic correlations appear to modify the nature of bands involved at $\Gamma$ point. DFT + DMFT calculations for the bulk states have shown one extra hole pocket at M point. Incoherent features seem to be possessed by mostly Co $d_{xz} + d_{yz}$ orbitals in the spectra of bulk CoSi. The existence of both coherent and incoherent features 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 $\omega \sim$ − 3 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.

Graphic abstract