Weak localization with a specific role of t symmetry (2D and 3D holes in tellurium)

The anomalous magnetoresistance in crystalline tellurium is analyzed for different p-type carrier dimensions: a bulk sample, size-quantized accumulation layers on different tellurium crystallographic surfaces, and tellurium clusters (tellurium embedded in a dielectric opal matrix). It is shown that the effect can be interpreted in all cases in terms of the theory of weak localization of noninteracting particles with inclusion of the specific features of the tellurium band spectrum, namely, fully lifted spin degeneracy, trigonal spectrum distortion, and a specific role played by the t symmetry in inter-valley scattering. The differences observed among the various manifestations of the weak localization effect are determined by the hole wave function phase-relaxation channel which is dominant in a particular case. A case is discussed where the time characterizing the inter-valley transition probability becomes comparable to the momentum relaxation time.