Tilt of the Electron Fermi Surface in Bi

Abstract

Many experiments show that the long axes of the three extremely prolate ellipsoids which represent the electron Fermi surface in bismuth are tilted ∼6° from the trigonal plane of the Brillouin zone; however, the sign of this tilt angle cannot be unambiguously obtained from the literature. We report results obtained from measurements of the de Haas-van Alphen and de Haas-Shubnikov effects and quadratic magneto-resistance which show that the sign of the tilt angle is positive in terms of the usual conventions, which are carefully defined. More explicitly, the long axis of each ellipsoid lies within the ∼18° angle made by a bisectrix direction and a $\Gamma L$ direction in the Brillouin zone. Our results are shown to agree with the most recent band calculations for Bi. Comparison of de Haas-van Alphen results on Bi and Sb samples, each with the same orientation as determined by x rays, shows that, independently of any convertion, the tilt angles of Bi and Sb have opposite signs. We also clarify the procedures for properly orienting a crystal of bismuth by observing either twinning planes or etch pits in the trigonal plane.