Adiabatic Mode Selection and Accuracy of Quantization of Ballistic Point Contacts
Recent experiments by van Wees et al.  and Wharam et al.  revealed that the two-terminal conductance of a narrow constriction is quantized in integer multiples of e2/πℏ (including spin degeneracy). The experiments were done on a two-dimensional electron gas (2DEG) in a AlxGa1-xAS/GaAs heterostructures for which the length of the constriction was smaller than the elastic and inelastic mean free paths. The constriction is regarded as a narrow strip, having its own n modes or “conduction channels”, connecting two wide regions that in turn are connected with negligible resistance to electron reservoirs. It has been pointed out  that such a quantization follows from the two-terminal Landauer [4–6] formula G = e2/πℏ ∑ ij Tij, for full transmission (∑i Tij = 1) in the conducting channels, i.e. for a ballistic constriction. Glazman et al.  have recently shown how an adiabatic (i.e. slowly varying) geometry of the constriction can very easily explain the quantization which is exact in the adiabatic limit. However, in most real samples the variations in the geometry of the confining walls are slow in the region where the constriction is narrowest but are abrupt near its termination. Accurate quantization therefore required good impedance matching between the point where adiabaticity is lost and the wide region that is connected to the constriction. Here it is shown, that in order to get a good impedance match one needs the highest transverse mode which arrives at the non-adiabatic opening to be sufficiently low compared with the maximal one supported at the opening. This mode selection can be achieved by an adiabatic constriction and/or by a potential barrier. These insights can be used to predict which conditions the conductance quantization will become accurate.
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