Spin surfaces and trajectories in valence bands of tetrahedral semiconductors

Abstract

Surfaces and trajectories traced out by spin vectors in spin space are calculated and systematized for holes in tetrahedral semiconductors. It is shown how various trajectories are related to the wave-function phases and amplitudes of the doubly degenerated heavy-mass, light-mass, or split-off bands. Relations between hole wave vectors and spin surface shapes are examined for high symmetry directions. The presented results may be useful in ultrafast spintronics, where both the spin state and the wave vector of a hole should be taken into account simultaneously in the description of the hole spin dynamics.

Spin properties of electrons in a quantum tube

“…However, as we shall see, in the presence of SO interaction the direction of the natural quantization axis is different. The spin surface represents all possible directions and magnitudes of the average spin in the spin space [12,15,18,19]. In the simplest case when the SO interaction is unimportant it reduces to the Bloch sphere [18].…”

“…The properties of spin surfaces in planar quantum wells were discussed earlier in Refs. [12][13][14][15].…”

Hole spin surfaces in A3B5semiconductors

“…It is characterized by three empirical parameters γ 1 , γ 2 , γ 3 , and by the strength ∆ of spin-orbit splitting between Γ 8 and Γ 7 bands at the point k = 0. H 0 is the main contribution in the elementary semiconductor valence-band Hamiltonian that represents the doubly degenerate heavy-mass (h), light-mass (l), and split-off (s) energy bands as well as the spin properties in these semiconductors [6]. In general, the total Hamiltonian (2) with the linear-k part H 1 included yields nonparabolic, nonspherical, and nondegenerate (except at some high symmetry points) energy bands.…”

“…However, for valence bands, due to strong spin-orbit interaction, the spin surfaces may substantially deviate from the sphere as shown recently in [5,6]. In an extreme case the spin surface may shrink to a line, for example, when the heavy-mass hole propagates in high-symmetry direction, especially in [001]-type directions.…”

“…In papers [5,6], spin properties of the tetrahedral semiconductors such as p-type silicon or germanium, the elementary cell of which possesses the inversion symmetry, was considered. In such semiconductors all bands are doubly degenerate all over the Brillouin zone.…”