Introduction to Mesoscopic Physics

by Joseph Imry

Overview

"Mesoscopic physics" refers to the physics of structures larger than a nanometer (one billionth of a meter) but smaller than a micrometer (one millionth of a meter). This size range is the stage on which the exciting new research on submicroscopic and electronic and mechanical devices is being done. This research often crosses the boundary between physics and engineering, since engineering such tiny electronic components requires a firm grasp of quantum physics. Applications for the future may include such wonders as microscopic robot surgeons that travel through the blood stream to repair clogged arteries, submicroscopic actuators and builders, and supercomputers that fit on the head of a pin. The world of the future is being planned and built by physicists, engineers, and chemists working in the microscopic realm. This book can be used as the main text in a course on mesoscopic physics or as a supplementary text in electronic devices, semiconductor devices, and condensed matter physics courses.

Product Details

ISBN-13:	9780195356373
Publisher:	Oxford University Press
Publication date:	02/13/1997
Series:	Mesoscopic Physics and Nanotechnology
Sold by:	Barnes & Noble
Format:	eBook
File size:	3 MB

About the Author

Weizman Institute

Table of Contents

1	Introduction and a Brief Review of Experimental Systems	3
1	Generalities	3
2	A Brief Description of Systems and Fabrication Methods	6
2	Quantum Transport, Anderson Localization	12
1	Basic Concepts	12
	Localization ideas	14
2	Thermally Activated Conduction in the Localized Regime	18
3	The Thouless Picture, Localization in Thin Wires and Finite Temperature Effects	21
4	The Scaling Theory of Localization and its Consequences	26
	General	26
	The case d [less than or equal] 2	27
	The case d > 2, the metal-insulator (M-I) transition	30
5	The Weakly Localized Regime	34
3	Dephasing by Coupling with the Environment, Application to Coulomb Electron-Electron Interactions in Metals	38
1	Introduction and Review of the Principles of Dephasing	38
2	Dephasing by the Electron-Electron Interaction	46
3	Review of Results in Various Dimensions	50
4	Dephasing Time vs. Electron-Electron Scattering Time	56
4	Mesoscopic Effects in Equilibrium and Static Properties	60
1	Introductory Remarks, Thermodynamic Fluctuation Effects	60
2	Quantum Interference in Equilibrium Properties, Persistent Currents	65
	Generalities, simple situations	65
	Independent electrons in disordered systems	71
	The semiclassical picture	75
	General results on ensemble-averaged persistent currents for constant N	80
	Semiclassical theory of spectral correlations, applications to rings	82
	Interaction effects on the persistent currents	84
5	Quantum Interference Effects in Transport Properties, the Landauer Formulation and Applications	89
1	Generalities, Remarks on the Kubo Conductivity for Finite Systems	89
2	The Landauer-type Formulation for Conductance in a Mesoscopic System and Some of its Generalizations	93
	Introduction: the "single-channel" case	93
	The multichannel Landauer formulation	96
	The Onsager-type relationship in a magnetic field: generalized multiterminal conductance formulas	103
3	Applications of the Landauer Formulation	107
	Series addition of quantum resistors, 1D localization	107
	Parallel addition of quantum resistors, A-B oscillations of the conductance	109
	On the universality of the conductance fluctuations	120
6	The Quantum Hall Effect (QHE)	124
1	Introduction	124
2	General Arguments	129
3	Localization in Strong Magnetic Fields and the QHE	133
4	Brief Remarks on the Fractional Quantum Hall Effect (FQHE)	139
7	Mesoscopics with Superconductivity	147
1	Introduction	147
2	Superconducting Rings and Thin Wires	151
3	Weakly Coupled Superconductors, the Josephson Effect and SNS Junctions	160
	The Bloch picture	160
	The Josephson junction and other weak links	163
4	Brief Remarks on Vortices	165
5	The Andreev Reflection, More on SN and SNS Junctions	167
8	Noise in Mesoscopic Systems	176
1	Introduction	176
2	Shot Noise for "Radiation" from a Reservoir	178
3	The Effect of Fluctuations in the Sink, the Equilibrium Limit	181
4	Low-Frequency (1-f) Noise	185
9	Concluding Remarks	191
	Appendices
A	The Kubo, Linear Response, Formulation	195
B	The Kubo-Greenwood Conductivity and the Edwards-Thouless Relationships	198
C	The Aharonov-Bohm Effect and the Byers-Yang and Bloch Theorem	200
D	Derivation of Matrix Elements in the Diffusion Regime	201
E	Careful Treatment of Dephasing in 2D Conductors at Low Temperatures	201
F	Anomalies in the Density of States (DOS)	202
G	Quasiclassical Theory of Spectral Correlations	204
H	Details of the Four-Terminal Formulation	207
I	Universality of the Conductance Fluctuations in Terms of the Universal Correlation of Transmission Eigenvalues	208
J	The Conductance of Ballistic "Point Contacts"	209
	References	211
	Index	231

Editorial Reviews

For researchers and graduate students in physics, chemistry, and electronic and optical engineering, Imry (physics, Weizmann Institute, Israel) explains concepts and tools to investigate systems that fall between the molecular and the bulk—generally a cluster of molecules that acts in many ways like a large molecule but has certain qualities unique to the size range. In particular he shows how the fundamental principles of quantum mechanics and statistical physics appear, and are amenable, to theoretical clarification and experimental examination in mesoscopic systems. Annotation c. Book News, Inc., Portland, OR (booknews.com)

"A propitious beginning for Oxford University Press's series Mesoscopic Physics and Nanotechnology. This is an area of physics in which there has been recent explosive development, made possible by nanofabrication methods and equipment, the development of which has been driven in turn by the technological goal of achieving ever denser digital electronic circuitry. As the physical limits of conventional electronic devices are approached, the understanding of the remarkable new physics of very small devices will be crucial for continued technological progress." —Michael Tinkham, Harvard University, in Physics Today

"Imry, who is one of the central figures in the development of the field, provides in this text a valuable overview of these new physical phenomena. . . .This interesting and relatively brief new book brings the reader into contact with some exciting developments in a very active area of condensed matter physics. It provides a ready reference to the main themes and results and belongs on the desks of all workers in this field." —Michael Tinkham, Harvard University, in Physics Today

"A key role in these developments [leading to the current work in mesoscopic physics] was played by Yoseph Imry, who has now written a book to share his insights. The time is right. Mesoscopic physics has reached a certain maturity, and many universities have included it as a course topic. It makes indeed a wonderful subject for students, since it provides real-life application of what they have learned in their quantum mechanics courses. Imry's book is the first comprehensive introduction to the field. . . .This is an excellent introduction to a new field of physics. It should appeal to teachers looking for a course that crosses the boundaries between traditional courses on statistical mechanics, quantum mechanics, and solid-state physics. I plan to use it myself for such a course in the near future. More advanced researchers will benefit from Imry's insightful qualitative explanations." —Journal of Statistical Physics

"The appearance of this introductory book is...quite timely. The author is one of the most active researchers in this field, so the reader is able to delve into a variety of problems related by a common base to study the interplay among the developed ingredients and to perceive the atmosphere of their formation. Moreover, many questions are unsolved so far, and the book promises to provide a view of where they are already substantiated." —Materials Research Bulletin

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