Quantum and Classical Ballistic Transport in Constricted Two-Dimensional Electron Gases

Abstract

An experimental and theoretical study of transport in constricted geometries in the two-dimensional electron gas in high mobility GaAs-AlGaAs heterostructures is described. A discussion is given of the influence of boundary scattering on the quantum interference corrections to the classical Drude conductivity in a quasi-ballistic regime, where the transport is ballistic over the channel widlh, but diffusive over its length. Additionally, results are presented of a recent study of fully ballistic transport through quantum point contacts of variable width defined in the two dimensional electron gas. The zero field conductance of the point contacts is found to be quantized at integer multiples of 2e /h, and the injection of ballistic electrons in the two dimensional electron gas is demonstrated in a transverse electron focussing experiment.l Introduction A variety of length scales governs the electron transport at low temperatures (see Table I). The mean free path /,. in a degenerate electron gas is determined by elastic scattering from stationary impurities. In homogeneous samples the classical transport can be described by the local Drude conductivity O D = ne 2 l e /mv r , with n the electron gas density, \ F the Fermi velocity, and m the electron effective mass. In a two-dimensional electron gas (2-DEG) this classical expression can also be written äs O D = (e 2 /h) kfl f , with k F -m\ F lh the Fermi wave vector. The Drude conductance G D of a 2-DEG channel of length L and width W is G D = (W\L)o D . In two dimensions the smallest System for which a conductivity can be defined is a square of side of order /,. The above expression for the conductance C D of a larger channel can thus be seen äs the result of the classical addition of such small squares in a (Wjl t ) by (L/4) array (see Fig. 1). It is clear that any correlation between the squares is neglected in this approach.It is now well known that such correlations are important because of quantum interference [1]. Constructive interference between time reversed backscattered electron waves leads to a conductivity decrease known äs weak localization. Clearly, a prerequisite for this quantum interference effect is that the electrons maintain their phase coherence over a lime τ^, long compared to the elastic scattering lime t, = l f /\ F .

Magnetoresistance effects in laterally confined n-GaAs/(AlGa)As heterostructures

“…The sharp negative magnetoresistance below 0.1 T is attributed to WL. Other workers have derived equations for the WL effect in the quasiballistic regime [8], though a detailed analysis is not carried out here due to the distorting effects of the UCF. Note, however, that we expect the fall-off to be a one-dimensional WL effect since the 2~ WL effect is predicted to saturate when the magnetic length LB becomes comparable to or smaller than the elastic scattering length, which occurs for B > 0.01 T i n these channels.…”