Magnetic-Field-Induced Surface States in Bismuth

Abstract

The microwave-impedance oscillations observed in Bi single crystals in a weak magnetic field (0-6 Oe at 32 GHz) are due to resonant transitions between surface quantum states. After a brief "minimal theory" description of such surface states, we present a detailed calculation of the surface impedance spectrum for Bi that allows us to accurately evaluate Fermi-surface parameters from the experimental data. Using the established Fermi-surface geometry of Bi, we determine the Fermi velocity, point by point, on the central cross section of the electron ellipsoid to an accuracy of better than 2%. Values range from a maximum of 10.1×${10}^7$ cm/sec in the binary ($C_2$) direction down to 7.8×${10}^7$ cm/sec at right angles to $C_2$. A line integral of the velocities around the cross section agrees exactly with the cyclotron mass, $(0.0077\mathrm{}\pm 0.0002)m_0$, as measured in the present experiments. The accurately known Fermi surface of Bi has made it possible for us to explore and verify interesting geometrical features of the resonance signals.