publication . Preprint . 2001

Quantum Phenomena in Low-Dimensional Systems

Geller, Michael R.;
Open Access English
  • Published: 13 Jun 2001
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
arXiv: Physics::Physics Education
free text keywords: Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Strongly Correlated Electrons
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[1] Physics of Low-Dimensional Semiconductor Structures, edited by P. Butcher, N. H. March, and M. P. Tosi (Plenum Press, New York, 1993).

[2] Nanotechnology, edited by G. Timp (Springer-Verlag, New York, 1999).

[3] G. J. Milburn, Schr¨odinger's Machines: The Quantum Technology Reshaping Everyday Life (W. H. Freeman and Company, New York, 1997).

[4] J. M. Ziman, Theory of Solids, 2nd ed. (Cambridge University Press, Cambridge, 1972).

B. Artifical Molecules [5] Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, Oxford, 1997).

[6] J. J. Sakurai, Modern Quantum Mechanics (The BenAnother new area of research is the study of pairs of jamin/Cummings Publishing Company, Menlo Park, quantum dots, which then can be thought of as artifi- 1985). cial molecules. Just as in natural molecules, bonds can [7] S. Olariu and I. I. Popescu, Rev. Mod. Phys. 57, 339 be formed between the atoms by electrons shared be- (1985). tween dots. These systems permit controlled studies of [8] S. Washburn, in Mesoscopic Phonomena in Solids, edited (at least some) basic molecular phenomena. One problem by B. L. Altshuler et al. (Elsevier Science Publishers, New of current interest is the magnetic properties of artifical York, 1991). molecules. [9] C. W. J. Beenakker and H. van Houten in Solid State Physics: Advances in Research and Applications, vol. 44, edited by H. Ehrenreich and D. Turnbull (Academic Press, San Diego, 1991).

C. Nanocrystals and Nanoparticles [10] D. C. Mattis, The Many-Body Problem: An Encyclopedia of Exactly Solved Models in One Dimension (World ScienThere is considerable interest in nanometer-scale crys- tific, Singapore, 1993). tals containing, say, from 103 to 106 atoms [29]. These [11] Z. N. C. Ha, Quantum Many-Body Systems in One Dimencan have structural, electronic, and optical properties sion (World Scientific, Singapore, 1996). very different than bulk solids. Spherical or nearly spher- [12] A. Zangwill, Physics at Surfaces (Cambridge University ical nanocrystals are sometines called nanoparticles. Press, Cambridge, 1988).

[13] G. Bastard, Wave Mechanics Applied to Semiconductor Semiconducting and insulating nanorystals have many Heterostructures (Les Editions de Physique, Cedex, 1988). similarities to quantum dots. In fact, the electronic prop- [14] C. Kittel, Introduction to Solid State Physics, 7th ed. (John erties are often the same, because in both cases the elec- Wiley and Sons, New York, 1996). tron is confined in all three directions. However the vi- [15] H. A. Fertig, in Perspectives in Quantum Hall Effects, brational properties can be quite different: A quantum edited by S. Das Sarma and A. Pinczuk (John Wiley and dot is not usually mechanically isolated from a bulk solid, Sons, New York, 1997). so it supports a continuum of low-frequency vibrational [16] See Search and Discovery article by G. B. Lubkin in Physics modes. But an isolated nanocrystal would have a dis- Today, July 1997, page 21. crete vibrational spectrum, much like that of a drum [17] The Quantum Hall Effect, edited by R. E. Prange and S. head. This means that any physical property involving M. Girvin (Springer-Verlag, New York, 1987). phonons will be very different than that in a macroscopic [18] J. K. Jain, Physics Today, April 2000, page 39. solid.

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