Magnetic focusing of electrons and holes in bismuth

Abstract

The electron and hole focusing effects in a magnetic field predicted by Pippard have been observed in bismuth. Two interlocking superconducting combs were evaporated onto the surface of a bismuth single crystal. The resistanceR(H) between the combs was measured with a superconducting voltmeter as a function of the magnetic fieldH applied parallel to the teeth of the combs. A local minimum in the resistance was observed when the magnetic field focused electrons or holes in extremal orbits between the teeth of different combs. A similar effect was observed when the combs were replaced by two parallel superconducting strips. In this case the dependence ofR(H) onH was in good qualitative agreement with the calculation of Gonçalves da Silva on a model whose Fermi surface was topologically equivalent to that of bismuth. From the values ofH at which the minima occurred we have deduced estimates forD _xe andD _ze , the diameters of the principal electron ellipsoid along the binary and trigonal axes. We findD _xe =(0.94±0.03)×10⁻² Å⁻¹ andD _ze =(1.35±0.04)×10⁻² Å⁻¹. These values lie somewhat below other values in the literature. This discrepancy may occur because each minimum inR(H) occurs at a field slightly belowH ₀, whereH ₀ is the field for which the diameter of the extremal electron trajectory is equal to the separation of the superconducting strips.