Quantum Interference Fluctuations in Disordered Metals

DEC 01, 1988

Phase coherence over thousands of lattice spacings in disordered metals can produce quantum interference effects in electrical resistance measured in very small devices.

DOI: 10.1063/1.881140

Richard A. Webb

Sean Washburn

In statistical physics one is trained to think about the properties of large ensembles of particles, and to calculate bulk properties by averaging over many microscopic configurations. Although the quantum mechanical properties of the individual constituents of a macroscopic object are important over some length scale (typically a few lattice spacings), they are usually not correlated across the whole object. We are, however, becoming acquainted with more and more disordered systems for which this effective length scale, at low temperatures, can be 100–10 000 times the characteristic microscopic scale; the correlation can involve more than $10^{11}$ particles. Such phenomena occur in an intermediate “mesoscopic” regime that lies between the microscopic world of atomic and molecular orbitals and the thoroughly macroscopic world where averages tell all. The wealth of novel quantum coherence phenomena recently observed in this intermediate size regime is the subject of this article.

References

1. R. Landauer, Philos. Mag. 21, 863 (1970).https://doi.org/PHMAA4
2. See the reviews by A. G. Aronov, Yu. V. Sharvin, Rev. Mod. Phys. 59, 755 (1987); https://doi.org/RMPHAT
Y. Imry, in Directions in Condensed Matter Physics, G. Grinstein, E. Mazenko, eds., World Scientific, Singapore (1986);
S. Washburn, R. A. Webb, Adv. Phys. 35, 375 (1986).https://doi.org/ADPHAH
3. A. Tonomura, N. Osakabe, T. Matsuda, T. Kawasaki, J. Endo, S. Yano, H. Yamada, Phys. Rev. Lett. 56, 792 (1986).https://doi.org/PRLTAO
4. N. B. Brandt, D. B. Gitsu, V. A. Dolma, Ya. G. Ponomarev, Sov. Phys. JETP 65, 515 (1987), and references cited therein.https://doi.org/SPHJAR
5. M. Büttiker, Y. Imry, R. Landauer, Phys. Lett. A 96, 365 (1983). https://doi.org/PYLAAG
Y. Gefen, Y. Imry, M. Ya. Azbel, Phys. Rev. Lett. 52, 129 (1984).https://doi.org/PRLTAO
6. R. A. Webb, S. Washburn, C. P. Umbach, R. B. Laibowitz, Phys. Rev. Lett. 54, 2696 (1985). https://doi.org/PRLTAO
V. Chandrasekhar, M. J. Rooks, S. Wind, D. E. Prober, 55, 1610 (1985).
S. Datta, M. R. Melloch, S. Bandyopadyay, R. Noren, M. Varizi, M. Miller, R. Reifenberg, Phys. Rev. Lett. 55, 2344 (1985).https://doi.org/PRLTAO
7. A. D. Stone, Phys. Rev. Lett. 54, 2692 (1985).https://doi.org/PRLTAO
8. A. D. Stone, Y. Imry, Phys. Rev. Lett. 56, 189 (1986).https://doi.org/PRLTAO
9. B. L. Al’tshuler, JETP Lett. 41, 648 (1985). https://doi.org/JTPLA2
B. L. Al’tshuler, B. I. Shklovskii, Sov. Phys. JETP 64, 127 (1986). https://doi.org/SPHJAR
P. A. Lee, A. D. Stone, H. Fukuyama, Phys. Rev. B 35, 1039 (1987). https://doi.org/PRBMDO
P. Lee, A. D. Stone, Phys. Rev. Lett. 55, 1622 (1985).https://doi.org/PRLTAO
10. Y. Imry, Europhys. Lett. 1, 249 (1986). https://doi.org/EULEEJ
P. A. Lee, Physica A 140, 169 (1986).https://doi.org/PHYADX
11. J. C. Licini, D. J. Bishop, M. A. Kastner, J. Melngailis, Phys. Rev. Lett. 55, 2987 (1985). https://doi.org/PRLTAO
S. Washburn, C. P. Umbach, R. B. Laibowitz, R. A. Webb, Phys. Rev. B 32, 4789 (1985).https://doi.org/PRBMDO
12. G. Timp, A. M. Chang, J. E. Cunningham, T. Y. Chang, P. Mankiewich, R. Behringer, R. E. Howard, Phys. Rev. Lett. 58, 2814 (1987).https://doi.org/PRLTAO
13. C. P. Umbach, C. van Haesendonck, R. B. Laibowitz, S. Washburn, R. A. Webb, Phys. Rev. Lett. 56, 386 (1986). https://doi.org/PRLTAO
W. J. Skocpol, P. M. Mankiewich, R. E. Howard, L. D. Jackel, D. M. Tennant, A. D. Stone, Phys. Rev. Lett. 56, 2865 (1986).https://doi.org/PRLTAO
14. F. P. Milliken, S. Washburn, C. P. Umbach, R. B. Laibowitz, R. A. Webb, Phys. Rev. B 36, 4465 (1987).https://doi.org/PRBMDO
15. A. D. Benoit, S. Washburn, C. P. Umbach, R. A. Webb, D. Mailly, L. Dumoulin, in Anderson Localization, H. Fukuyama, ed., Springer‐Verlag, Heidelberg (1988).
16. B. L. Al’tshuler, D. E. Khmel’nitskii, JETP Lett. 42, 359 (1985). https://doi.org/JTPLA2
D. E. Khmel’nitskii, A. I. Larkin, Sov. Phys. JETP 64, 1075 (1986). https://doi.org/SPHJAR
A. I. Larkin, K. A. Matveev, Sov. Phys. JETP 66, 580 (1987).https://doi.org/SPHJAR
17. S. B. Kaplan, Surf. Sci. 196, 196 (1988). https://doi.org/SUSCAS
R. A. Webb, S. Washburn, C. P. Umbach, Phys. Rev. B 37, 8455 (1988).https://doi.org/PRBMDO
18. S. Washburn, H. Schmid, D. P. Kern, R. A. Webb, Phys. Rev. Lett. 59, 1791 (1987).https://doi.org/PRLTAO
19. B. L. Al’tshuler, B. Z. Spivak, JETP Lett. 42, 447 (1985).https://doi.org/JTPLA2
20. A. Benoit, C. P. Umbach, R. B. Laibowitz, R. A. Webb, Phys. Rev. Lett. 58, 2343 (1987). https://doi.org/PRLTAO
W. J. Skocpol, P. M. Mankiewich, R. E. Howard, L. D. Jackel, D. M. Tennant, A. D. Stone, Phys. Rev. Lett. 58, 2347 (1987).https://doi.org/PRLTAO
21. Y. Isawa, H. Ebisawa, S. Maekawa, in Anderson Localization, H. Fukuyama, ed., Springer‐Verlag, Heidelberg (1988).
J. Phys. Soc. Jpn. 56, 25 (1987). https://doi.org/JUPSAU
M. Büttiker, Phys. Rev. B 35, 4123 (1987).https://doi.org/PRBMDO
22. H. U. Baranger, A. D. Stone, D. di Vincenzo, Phys. Rev. B 37, 6521 (1988). https://doi.org/PRBMDO
C. L. Kane, P. A. Lee, D. diVincenzo, Phys. Rev. B 38, 2995 (1988). https://doi.org/PRBMDO
D. P. diVincenzo, C. L. Kane, Phys. Rev. B 38, 3006 (1988). https://doi.org/PRBMDO
S. Hershfield, V. Ambegaokar, Phys. Rev. B 38, 7909 (1988).https://doi.org/PRBMDO
23. M. Büttiker, IBM J. Res. Dev. 32, 317 (1988). https://doi.org/IBMJAE
M. Büttiker, Phys. Rev. Lett. 56, 1761 (1986). https://doi.org/PRLTAO
A. D. Benoit, S. Washburn, C. P. Umbach, R. B. Laibowitz, R. A. Webb, Phys. Rev. Lett. 56, 1765 (1986).https://doi.org/PRLTAO
24. R. A. Webb, S. Washburn, H. J. Haucke, A. D. Benoit, C. P. Umbach, F. P. Milliken, in Physics and Technology of Submicron Structures, Springer‐Verlag, Heidelberg (1988).
25. C. P. Umbach, P. Santhanam, C. van Haesendonck, R. A. Webb, Appl. Phys. Lett. 50, 1289 (1987).https://doi.org/APPLAB

More about the Authors

Richard A. Webb. IBM Thomas J. Watson Research Center, Yorktown Heights, New York.

Sean Washburn. IBM Thomas J. Watson Research Center, Yorktown Heights, New York.