Electronic structure of quasi-one-dimensional superconductor K$_2$Cr$_3$As$_3$ from first-principles calculations

The electronic structure of quasi-one-dimensional superconductor K$_2$Cr$_3$As$_3$ is studied through systematic first-principles calculations. The ground state of K$_2$Cr$_3$As$_3$ is paramagnetic but very close to a ferromagnetic instability. Close to the Fermi level, the Cr-3d$_{z^2}$, d$_{xy}$, and d$_{x^2-y^2}$ orbitals dominate the electronic states, and three bands cross $E_F$ to form one 3D Fermi surface sheet and two quasi-1D sheets. The electron DOS at $E_F$ is less than 1/3 of the experimental value, indicating an intermediate electron renormalization factor around $E_F$. Despite of the relatively small atomic numbers, the antisymmetric spin-orbit coupling splitting is sizable ($\approx$ 60 meV) on the 3D Fermi surface sheet as well as on one of the quasi-1D sheets. Finally, the imaginary part of bare electron susceptibility shows large peaks at $\Gamma$, suggesting the existence of large ferromagnetic spin fluctuation in the compound.