Tunneling in low-barrier GaAs/AlxGa1−xAs/GaAs heterostructures has been systematically investigated over a wide range of barrier heights and thicknesses. Measured conductance data have been compared with tunnel conductances calculated with and without the image potential correction. Experimental evidence is found for the validity of the static image correction in the limit of large tunneling times, and for the occurrence of dynamic effects in the limit of short tunneling times.
We report an experimental observation of impurity-induced conductance dips in quantized channels as predicted by previous theoretical studies. Our experiments use quantum point contacts on a two-dimensional electron gas in a modulation-doped GaAs/Al Gai -"As heterostructure. The electron gas has a sheet density of 1.2x10" cm 2 and a mobility of 4. 6x10' cm2/Vs, measured at 50 mK. Our data, which are qualitatively very similar to those calculated with use of a two-dimensional Anderson model, strongly suggest that we are observing both the erosion of conductance quantization, and localization in the presence of an impurity-induced random potential. Conductance measurements (van Wees et al. ' and Wharam et al. ) with so-called quantum point contacts (QPC) on a two-dimensional (2D) electron gas in modulation-dopedGaAs/A1, Gai "As heterostructures have demonstrated the existence of plateaus at integer multiples of the elementary conductance Go q /xh. The plateaus observed in those experiments are fairly flat and well defined, pointing to nearly ideal conditions for their observation. It is therefore of great interest to understand what "ideal" means in this particular context, and how various factors such as the potential distribution in the constriction affect the quantization. As impurities, intentional or not, are unavoidable, it is of particular interest to investigate their influence. One suspects for example that, since the remote doping layer in the Al"Gai -, As affects the mobility of the 2D electron gas, it will also affect the quantization in some way. The worst case, one may think, would be that of unintentional impurity centers being located directly in the confined channel.Such questions are now attracting widespread interest among theoreticians. Different groups have recently provided an extensive study of the case of an impurity (attractive or repulsive) being located in the confined channel. From a set of interesting results, these groups have shown that attractive impurities, in particular, exhibit a clear signature in the form of a deep dip appearing at the end of each conductance plateau, followed by a sharp rise to the next plateau as the channel width is increased. Using a somewhat different approach, other theoreticians have studied the crossover from ballistic to diffusive transport in quantized channels as a function of disorder produced by a random, attractive impurity potential. Their results show a rounding of the conductance steps with increasing disorder, loss of the quantization in units of Go, and the occurrence of pronounced conductance dips at each new channel opening. These finding are consistent with the single-impurity case cited above. Kander, Imry, and Sivan interpret the conductance dips as a localization e6'ect occurring each time a new channel is opened. This Rapid Communication reports experimental observation of impurity-induced conductance dips in quantized channels as predicted by the authors cited above. Our 2p, m C) 3 (3 C9 .8 0.4 0 -0.4 g4 gf r l . / V (V) FIG. 1. Point-...
Gueret, Blanc, Germann, and Rothuizen Reply: In the Comment [1] on our Letter [2], Beton, Eaves, and Main claim that our "observations are more consistent with an increase in the potential in the quantum well due to the electrostatic effect of the gate voltage than with a gatecontrolled quantum confinement effect," that ''the peaks in the conductance are more likely to be due to transitions between states localized by random variations in the lateral potential," and that ''the experiment described shows only an overall shift of the conductance peaks with increasing negative gate bias." The authors of the Comment conclude that our observations are to be interpreted as transitions through localized (donor) states without gate confinement, and refer to their work with other authors (Dellow et ai [3]) for this recently proposed model.Although a model based on transitions through localized states has (in our opinion as well) its own range of validity, it is certainly not the universal explanation for features in conductance or liV) data. In particular, the presence of potential fluctuations is not a sufficient condition to preclude gate confinement and its observation. Channel size is quite important in this respect.It may therefore be necessary to begin the discussion by stressing a significant difference between our work [2] and that of Dellow et al. [3], namely, the difference in the lateral device and channel sizes reported.The device reported in [3] has a designed (lithographic) size of 1 ^m, and can be squeezed with a gate voltage of -5 V to a channel diameter estimated from the data in [3] to be about 300 nm. With such large sizes (and large also compared to the spatial scale of potential fluctuations), there is virtually no hope of observing gate confinement. The device behavior is in this case most likely dominated by the local nonuniformities of the potential landscape, as indeed reported in [3].In contrast, our work [2] deals with designed (lithographic) sizes in the 0.4-to 0.3-pm range, which can further be squeezed to channel sizes smaller than 100 nm with a gate voltage of -2 to -3 V. This is a spatial scale which is now approaching that of possible potential fluctuations. Moreover it yields measurable confinement energies of the order of a few meV (about 10 times larger than they would be in the device reported in [3]).In terms of both confinement energies and channel size, our work [2] deals therefore with quite a different regime from that reported in [3]. And although nonuniformities certainly play a role in our case as well (as noted in our Letter [2]), we find that the prominent features observed and their dependence on channel squeezing (particularly the appearance and gradual evolution with gate voltage of the 1-nA current plateau) provide good evidence for the proposed gate confinement effect. Local fluctuations of the potential are significant in our case insofar as they affect the mode ladder in the dot, which makes a direct and detailed quantitative comparison with idealized models difficul...
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