Open-Orbit Resonances in Tin

We have studied the resonant absorption of ultrasonic waves by electrons executing open orbits in pure single crystals of tin at low temperatures. Two types of resonance were observed, associated with periodic and aperiodic open orbits. The resonant oscillations arising from periodic open orbits in the [110] directions have a period consistent with the zone dimensions and generally narrow with increasing ultrasonic frequency as predicted by the theory. Some of these resonances, however, have an anomalous line shape, caused by interference with geometric oscillations. The other type of resonance is associated with generally aperiodic open orbits on the zone 4(a) hole Fermi surface. These resonant oscillations generally have a short period which varies rapidly with magnetic-field direction and is consistent with the zone dimensions. The width of the resonances decreases anomalously slowly with ultrasonic frequency, probably because of an inherent width associated with the aperiodicity of the orbits.