Spin-Orbit Interaction in Graphite

Abstract

Using symmetry arguments, the effective-mass Hamiltonian including spin-orbit interaction is derived for energy bands with extrema near the vertical edge of the hexagonal prism which represents the Brillouin zone of graphite. The energy bands in the plane normal to the vertical edge are described by k\ifmmode\cdot\else\textperiodcentered\fi{}p perturbation theory, whereas along the edge a Fourier expansion is used for all the matrix elements. It is shown that spin-orbit interaction lifts all band degeneracies (other than the Kramers degeneracy), and affects the graphite Fermi-surface topology at the Brillouin-zone boundary ${k}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{{c}_{0}}$, where two de Haas-van Alphen periods are predicted. Magnetic energy levels for a static magnetic field H\ensuremath{\parallel}c are obtained by solution of the effective-mass Hamiltonian. Selection rules for infrared interband transitions are discussed. An evaluation of the spin-orbit band parameters is suggested by analysis of structure in the low-quantum-limit magneto-reflection data and of the low-frequency de Haas-van Alphen oscillations.