Ballistic Transport in Quasi-One-Dimensional Structures

Abstract

The split-gate structure illustrated in Plate 1, and modifications thereof, have been fabricated on a variety of high-mobility heterostructures grown by Molecular Beam Epitaxy at the Cavendish Laboratory. The lithographic length of the split-gate channel was defined to be 0.3 µm whilst the defined channel width was 0.5 µm. The significance of the low temperature high-mobility behaviour is to be seen immediately. The eigenstates of momentum are extremely long-lived and give rise to elastic lengths which can be in excess of several microns. Furthermore the inelastic length, which can be extracted from physical phenomena such as universal conductance fluctuations (Thornton 1987) or Aharanov-Bohm oscillations (Ford 1989), is also of the same order of magnitude. Electrons therefore pass ballistically through the narrow constriction, defined by the application of a negative bias to the gate electrodes, the only scattering being specular scattering from the side walls of the confining potential. Furthermore the Fermi wavelength of the two-dimensional electron gas (2DEG), which is given by ${{\lambda }_{f}} = \sqrt {{(2\pi /{{n}_{s}})}}$ and is of the order of 50 nm, is comparable to the effective channel width in these devices and hence the quantum nature of the electrons should be significant.