We present a semiclassical theory of weak disorder effects in small structures and apply it to the magnetic response of non‐interacting electrons confined in integrable geometries. We discuss the various averaging procedures describing different experimental situations in terms of one‐ and two‐particle Green functions. We demonstrate that the anomalously large zero‐field susceptibility characteristic of clean integrable structures is only weakly suppressed by disorder. This damping depends on the ratio of the typical size of the structure with the two characteristic length scales describing the disorder (elastic mean‐free‐path and correlation length of the potential) in a power‐law form for the experimentally relevant parameter region. We establish the comparison with the available experimental data and we extend the study of the interplay between disorder and integrability to finite magnetic fields.
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October 1996
Research Article|
October 01 1996
Integrability and disorder in mesoscopic systems: Application to orbital magnetism
Klaus Richter;
Klaus Richter
Institut für Physik, Memminger Strasse. 6, 86135 Augsburg, Germany
Max‐Planck‐Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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Denis Ullmo;
Denis Ullmo
Bell Laboratories, Lucent Technologies, 1D‐265, 600 Mountain Avenue, Murray Hill, New Jersey 07974‐0636
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Rodolfo A. Jalabert
Rodolfo A. Jalabert
Université Louis Pasteur, IPCMS‐GEMME, 23 rue du Loess, 67037 Strasbourg Cedex, France
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J. Math. Phys. 37, 5087–5110 (1996)
Article history
Received:
April 23 1996
Accepted:
June 19 1996
Citation
Klaus Richter, Denis Ullmo, Rodolfo A. Jalabert; Integrability and disorder in mesoscopic systems: Application to orbital magnetism. J. Math. Phys. 1 October 1996; 37 (10): 5087–5110. https://doi.org/10.1063/1.531677
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