Influences of spin-orbit coupling on Fermi surfaces and Dirac cones in ferroelectriclike polar metals

Based on first-principles calculations and $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ effective models, we report physical properties of ferroelectriclike hexagonal polar metals with $P{6}₃mc$ symmetry, which are distinct from those of conventional metals with spatial inversion symmetry. Spin textures exist on the Fermi surface of polar metals (e.g., ternary LiGaGe and elemental polar metal of Bi) and spin-momentum locking exist on accidental Dirac cones on the sixfold rotational axis, due to the spin-orbit coupling and lack of inversion symmetry in polar space group. This effect has potential applications in spin-orbitronics. Dirac points are also predicted in LiGaGe.