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Phase coherence length of electron waves in narrow AlGaAs/GaAs quantum wires fabricated by focused ion beam implantation
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12.In wire No. 44, is only 1.6. In such a short wire, the resistance due to the weak localization may differ from that in long wires. Santhanam calculated the effect of boundary conditions in short wires (Ref. 13). In our quantum wire, the end of the wire is connected with wide 2D gas and the electron waves would retain its phase over the distance in the 2D gas [see Eq. (3) in Ref. 13]. On the other hand, the AA theory and the BvK theory are for long wires [Eq. (4) in Ref. 13]. According to his calculation, the effect of the boundary condition in our case affects the estimation of by only ∼10%, which is almost negligible.
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