We have fabricated high-mobility, one-dimensional wires in GaAs-AlGaAs heterostructures and measured the resistance as a function of magnetic field and temperature. Because of the size of the devices and the high mobility, only a few channels carry the current at 35 mK with minimal scattering. Fluctuations in the resistance as a function of magnetic field due to quantum interference are observed for 0 &~, r & 300, where co, is the cyclotron frequency and r is the scattering time, superimposed upon Shubnikov-de Haas oscillations and the Hall eA'ect.PACS numbers: 72. 15.Gd, 72.90.+y, 73.60.Aq It is now technologically feasible to fabricate devices in GaAs-A1GaAs heterostructures which are comparable in width to the electron wavelength, and yet possess high mobility. ' Such devices provide a unique opportunity to investigate the role of quantum interference (QI) and the quantized Hall efrect in transport, because phase coherence is maintained on the length scale of a device, and because the role of current-carrying edge states is exaggerated. The following describes our measurements of the temperature dependence of the magnetoresistance of wires fabricated in modulation-doped GaAs-AlGaAs which vary in length from 700 nm to 4.7 pm, and are estimated to be 220-75 nm wide. The carrier density determined from the Hall eAect is n = (2.0-2.6) x 10'' cm corresponding to a Fermi wavelength of =(2'/n) '~= 50-56 nm, while the mobility p at 4 K is larger than 3.3X10 cm /V s, so that the elastic mean free path L, =hp/ekF is greater than 1.6 pm. Thus, the width of the sample is comparable to an electron wavelength, while the distance between voltage probes is less than L,. Because of quantization in the transverse direction, the current is carried by only a few ( & 8) channels (or transverse subbands) at the Fermi energy with minimal scattering. Consequently, we have measured the electrical resistance associated with a few channels in an electron-wave guide.Fluctuations in the resistance are observed as a function of 0 for 0~co, z.~3 00, where m, is the cyclotron frequency and r is the scattering time, concomitantly with Shubnikov-de-Haas oscillations and the quantum Hall eA'ect. The fluctuations are correlated and the amplitude is so large at 35 mK that negative dynamic resistance is observed. The fluctuations change to a lower frequency of oscillation and smaller amplitude in the extreme magnetic quantum limit where only the N =0 Landau level is filled. We tentatively propose that the fluctuations in the resistance of the wire are due to the Aharonov-Bohm eAect, and that the change in the typical frequency is indicative of change with magnetic field in the width of the distribution of electron trajectories across the waveguide. Recent experiments have demonstrated QI in magnetotransport of disordered metals, and of silicon inversion layers, but have been exclusively concerned with the quasi one-dimensional (QI D) regime L, «L, W & L&, where L is the sample length, W is the width, and L& is the phase coherence length, for ...
