Dimensional crossover of Shubnikov–de Haas oscillations in thin films of gray tin

Abstract

We have studied the Shubnikov--de Haas oscillations in n-type gray tin films in which several size-effect-quantized subbands are relevant. The observed oscillations at oblique magnetic-field angles become increasingly two-dimensional in character as the film thickness decreases. In addition, frequencies associated with nonextremal cross sections of the Fermi surface are observed.