Anomalous influence of a small amount of impurities on the longitudinal Shubnikov–de Haas oscillation amplitude in bismuth

Abstract

Longitudinal magnetoresistivity components ρ yy ( y) of pure and tin-doped (0.2, 1 and 10 ppm tin) bismuth single crystals were measured in magnetic fields up to 5 T at several fixed temperatures between 1.2 and 25 K. In each of the samples, except 10-ppm tin-doped one, the longitudinal Shubnikov–de Haas (SdH) oscillation became largest in amplitude at temperatures around 15, 12 and 8 K, respectively. Then, the amplitude became smaller as the temperature decreased. In the case of 10-ppm tin-doped bismuth, on the other hand, the SdH oscillation increased in amplitude markedly as the temperature was decreased. To understand this anomalous temperature dependence of the SdH oscillation amplitude, we carried out simple numerical simulations. We positively demonstrated that the three-phonon processes of phonon–phonon collisions caused the inter-Landau level transition of carriers. We also found the reason why the longitudinal SdH oscillation amplitude of 10-ppm tin-doped sample became larger with decreasing temperature in spite of the collision broadening of Landau levels.