Hole spin precession in semiconductors: Clifford algebra approach

Recently the Clifford (geometrical) algebra was addressed to describe dynamical properties of electron spin in semiconductors (Dargys 2009 Phys. Scr. 79 055702). In this paper, the Clifford algebra is used to investigate heavy and light hole spins in valence bands of cubic semiconductors. Owing to strong spin-orbit interaction in the valence band, the precession trajectories of hole spin polarization are ellipses, or even lines, rather than circles as usually found in the case of electrons. The paper shows how one can investigate the valence band spectrum and free-hole spin precession trajectories within a framework of the Clifford algebra Cl4,1. General formulae that describe free heavy- and light-mass hole spin precession are presented.