Anomalous Skin Effect in Bismuth

High-frequency (23.5-kMc/sec) surface resistance measurements have been made on plane surfaces of single-crystal bismuth at 2°K as a function of orientation. It has been ascertained that extreme anomalous skin effect conditions prevail, allowing details of the Fermi surface to be deduced from Pippard's theory. In Shoenberg's model of the electron band, components of the inverse effective-mass tensor divided by the Fermi energy are found to be $\frac{{\alpha }_1}{E_e}=9.10\mathrm{}$, $\frac{{\alpha }_2}{E_e}=0.088\mathrm{}$, $\frac{{\alpha }_3}{E_e}=4.7\mathrm{}$, and $\frac{{\alpha }_4}{E_e}=0.38\mathrm{}$ (in units of ${10}^3$/ev). These results are in essential agreement with values obtained from de Haas-van Alphen experiments and cyclotron resonance. The number of ellipses is definitely established to be six and the number of electrons found to be $N=5.5\mathrm{}\times {10}^{17}/{\mathrm{cm}}^3$. The parameters for the two hole ellipsoids are found to be $\frac{{\beta }_1}{E_h}=\frac{{\beta }_2}{E_h}=1.5\mathrm{}$ and $\frac{{\beta }_3}{E_h}=0.12\mathrm{}$. Assuming Shoenberg's value $E_e=0.0177\mathrm{}$ ev, we calculate $E_h=0.00112\mathrm{}$ ev from specific heat data. It is also found that the reflection of carriers from the surface of the sample is predominantly specular in contrast to diffuse reflection found in other metals.