Quantum Localization in Amorphous W-Re Alloys

Abstract

The resistance of amorphous W-Re wires between 2 and 20 °K has been measured. Wires with a resistance of approximately 10 kft show a different temperature dependence from that of wires with a resistance of over 200 k£2. The latter show a relative increase in resistance as the temperature is decreased or the magnetic field is increased. These wires also show an anomalous dependence of resistance on width and length. These results are discussed in the perspective of Thouless's suggestion of maximum metallic resistance.Thouless 1 has proposed that the temperature and length dependence of the conductance of a metallic wire deviates from its usually expected behavior when the resistance of the sample exceeds some critical value. This value ranges from 10 to 30 kS2. Similar ideas have been advanced byAdkins, 2 Licciardello and Thouless, 3 and Abrahams et al. 4 Several authors have searched for quantum localization in wires 5,6 and in composite materials. 7 We have carried out a series of electrical resistance measurements on amorphous W-Re alloys. Our samples show, qualitatively, the deviations predicted by Thouless. In addition, we have measured the temperature dependence of the resistance in a magnetic field and find enhanced magnetoresistance below 20 K. The magnetic-field dependence of quantum localization in metallic wires has not been predicted theoretically.We chose the amorphous alloys for a number of reasons. Because of positional disorder, we expect localization to be present. The resistivity of the amorphous samples is usually high. This has significant advantages in the fabrication of high-resistance metallic wires. The temperature dependence of the resistivity is generally small, so that small changes can be followed readily. In addition, the amorphous films can be deposited to yield relatively smooth films with little or no granularity that is characteristic of polycrystalline films. We chose the amorphous W-Re alloys for their stability to crystallization and general ability to withstand handling during the fabrication of the wires. These alloys have a superconducting-transition temperature which can be varied with composition. We used the superconducting transition temperature as a monitor of our film quality. Our films are nominally only 50 A thick and we were concerned about oxidation or other deleterious effects during the fabrication of the relatively high-resistance wires. Observing the same superconducting transition temperature in the high-and low-resistance films was therefore a reassuring sign that the quality of the highresistance wire had not been changed during fabrication.The films were grown by electron-beam evaporation onto oxidized silicon substrates. 8 The details of the microstructure and growth technique have also been discussed in Ref. 8. With electron-beam lithography and ion milling 9 the films were cut into wires with two types of widths. In one case, the width was varied between approximately 700 to 5000 A and in the other it was 20 pirn. The resistivity of the films measured at ...

Anderson Localization in the Seventies and Beyond

“…A mathematical argument to this effect was given at about the same time by Goldsheid. 32 Experimental evidence began to accumulate for a crossover from metallic behavior in thin wires as the temperature was lowered, [33][34][35] although it was clear that in these experiments a simple Anderson theory did not work, because interactions between electrons were playing a significant role. The one-dimensional case was worked out in more detail by Anderson et al 36 At this level, the scaling theory tells us little about what happens in two dimensions, since the dependence on L cancels out.…”

Resistance of quasi-one-dimensional wires

“…The identification of the physical conditions under which the results of Thouless 2 should be valid and those that would have been present in the experiments [6][7][8][9] done to verify his results, calls for new experiments under controlled conditions of disorder and temperature to study in detail the roles of inelastic scatterings from TS's and phonons separately in the electrical transport in quasi-1D systems. This should give more insight into the microscopic details of electron diffusion in the backdrop of localization.…”

“…This contention was however not borne out by experiments [4][5][6][7][8][9] which showed considerably less effect of localization.…”

“…[1][2][3][4][5][6][7][8][9][12][13][14][15][16][17][18][19][20][21]23 A fresh look at the results shows that the questions as to which of these effects dominates in the wires, and what is the magnitude of its influence on resistance, remained unresolved. We have investigated these problems which are relevent to basic aspects of localization in quasi-one dimension.…”

“…The experiments [4][5][6][7][8][9]12 showed that ⌬R/R 0 depends on A and T as A Ϫ1 and T Ϫ1/2 , respectively. Interestingly, both the interaction theory of Altshuler et al 13 with i ϭ ee and the localization theory of Thouless 2 with i ϭ TS yield the A and T dependence of ⌬R/R 0 as A Ϫ1 and T Ϫ1/2 , respectively.…”