Michael L. Roukes

Electron-Boundary Scattering in Quantum Wires

To reduce the dimensionality of an electronic system it must be confined within artificially imposed boundaries. In the most idealized consideration of the problem, the properties of confined electrons depend solely upon the volume containing them. In all real systems, however, the characteristics of the boundaries themselves play a significant role in the physics observed. Recent advances in epitaxial growth techniques now permit nearly ideal heterointerfaces to be created over appreciable areas. But even for these, the crystallographic (and therefore the electronic) properties at the surfaces are quite different that those of the bulk. Recent dramatic demonstrations of surface reconstructions obtained through scanning tunneling microscopy provide a particularly striking example. However the more general situation is even far from this ideal. Any real boundary, when viewed over a large enough area, always reveals randomness. In the case of the best epitaxially-grown interfaces this will be manifested as a finite domain size for the last few atomic layers, as schematically depicted in Fig. 1 (left). The edges of these domains delineate random patches of surfaces in registry with the underlying crystal. A quantum well between two such interfaces would be characterized by a thickness which varies stochastically across the growth plane.

Granularity in Narrow Wires: Conductance Fluctuations, Diffuse Boundaries and Junction Scattering

Many factors determine the electrical conductivity of a narrow wire. In a weakly disordered system we can begin with the Drude conductivity, σ=ne2τ/m, and add corrections which take account of various aspects of transport not included in this simple expression (see Fig. 1). For instance, disorder induced corrections arise from quantum interference and electron-electron interaction, generally lowering the conductivity. The interference arises because of coherent backscattering of electrons and reduces the diffusion coefficient below the classical result (D = vF l /2 for specular scattering) while the electron-electron interaction lowers the density of states at the Fermi energy. We can rewrite the Drude expression in terms of the diffusion coefficient, D, and the density of states, N(EF), as σ = e2DN(EF) and provided the corrections are small, δσ/σ ~ δD/D + δN/N(EF), so that the two are additive.

Ballistic Electron Transport in a Gated Constriction

It is now clear that the conductance of a short, narrow constriction in a 2DEG is quantised in units of 2e2/h1to8. This quantisation has so far only been demonstrated in short, split-gate FETs9 in which the width of the constriction can be continuously varied thereby changing the number of occupied quantum channels (subbands). Squeezing the constriction reduces the number of i occupied subbands and the resistance increases in a step like fashion with plateaus at values of R=h/2ie2. Split gates have been used in various configurations to demonstrate the magnetic depopulation of 1D subbands10, electron focussing11 and the non-additivity of ballistic resistors12. In this paper we show that the same quantisation exists in devices of constant width but variable carrier concentration (Fermi energy) and we discuss preliminary results from two devices of different aspect ratio.

Electron Waveguide Junctions: Scattering from a Microfabrication-Imposed Potential

In quantum wires, ultranarrow conduction channels having very low disorder, electrons can scatter from potentials which are radically different from those encountered in the bulk. Entirely new types of scattering potentials can be created by microfabrication, since ballistic devices having overall dimensions much smaller than the transport mean free path, and widths only slightly larger than one electron wavelength, can now be fabricated.1