Shubnikov-de Haas Effect in Bismuth

The oscillatory component of the transverse magnetoresistance of single crystals of bismuth has been measured at 1.15°K. The magnetic field range was 700 to 23 000 G. Measurements were taken in the three principal planes. The experimental results may be explained on the basis of two sets of carriers. No evidence was found for the third and fourth carriers reported recently. For holes we find ${{\beta }_{11}}^2=75.4\mathrm{}\times {10}^{+28\mathrm{}}{\left({E_F}^h\right)}^2$ ${\mathrm{erg}}^{-2\mathrm{}}$, ${\beta }_{11}{\beta }_{33}=7.25\mathrm{}\times {10}^{+28\mathrm{}}{\left({E_F}^h\right)}^2$ ${\mathrm{erg}}^{-2\mathrm{}}$; for electrons, ${\alpha }_{11}{\alpha }_{33}=23.3\mathrm{}\times {10}^{30}{\left({E_F}^e\right)}^2$ ${\mathrm{erg}}^{-2\mathrm{}}$, and the tilt angle is 4°. Here $E_F$ is the Fermi energy measured in ergs. The effects of spin splitting of hole Landau levels is observed at 70° from the $z$ axis, from which we find $g_3\cong 62$ (assuming $g_1\ll g_3$).