FIGURE 4 Magnetoresistance of an evaporated aluminum film 20 nm thick, measured at temperature T=4 K. From Gordon.43

is negligible in these data but must be taken into account to understand the magnetoresistance at lower temperatures.42,43

Figure 5 shows the magnetoresistance of a drawn platinum wire 150 nm in diameter and 2.5 mm long at three temperatures in the range from 1.5 K to 4 K.45 These data again can be explained by the weak localization type of quantum interference effect. Despite the fact that the wire here is narrower than the 1-D sample in Figure 4, the interpretation in this case involves a three-dimensional (bulk) theory, which is a reflection of the difference in materials parameters between the platinum and aluminum samples.

It is interesting to note that platinum wires as thin as 8 nm have been made by the same technique as the sample in Figure 5.46 In this procedure, the wire is drawn while it is encased in a silver supporting matrix, which is subsequently etched away. As yet, however, there have been no successful attempts to attach leads to these ultrathin specimens, so the electrical properties have not yet been measured.

A quantum interference effect related to the weak localization effects discussed above was first observed in 1981 by Sharvin and Sharvin47 using a thin magnesium film deposited on a fine quartz fiber as shown in Figure 6. The electrical resistance of this sample was found to depend periodically on the magnetic flux through the hole in the magnesium cylinder in a fashion that is reminiscent of the classic Aharanov-Bohm effect. In this case, however, the observed period is equal to h/2e, which is half the normal flux quantum.48 More recently, measurements on small one-dimensional rings



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