Electronic structure modelling in support of Symmetries of Spin-Splitting Induced by Spin-Orbit Coupling in Non-magnetic Crystals

The files presented in this repository is in support of the manuscript titled "Symmetries of Spin-Splitting Induced by Spin-Orbit Coupling in Non-magnetic Crystals". Spin-orbit coupling leads to splitting of otherwise spin-degenerate bands in noncentrosymmetric materials, even if time-reversal symmetry is present. We utilize point group representations and electric/eletrotoroidal multipoles to illustrate that four different types of SOC terms (Rashba, Dresselhaus, Weyl, and Ising) can emerge in periodic solids. We construct reciprocal-space energy expressions for each type of SOC-induced splitting of opposite-spin bands, and follow a similar procedure to also obtain minimal tight-binding models that capture all types of spin-splittings for subgroups of the two parent groups m-3m and 6/mmm. We also carry out DFT calculations to better visualize the spin-splitting multipoles in complex materials systems. Broadly speaking, our work provides a basis for studying superconductivity and other collective electronic phenomena that are impacted by SOC-induced band splittings in noncentrosymmetric materials.