ScienceWeek

SOLID-STATE PHYSICS: ON INTRINSIC LOCALIZED ENERGY MODES

The following points are made by D.K. Campbell et al (Physics Today 2004 January):

1) In solid-state physics, the phenomenon of localization is usually perceived as arising from extrinsic disorder that breaks the discrete translational invariance of the perfect crystal lattice. Familiar examples include the localized vibrational phonon modes around impurities or defects (such as atomic vacancies or interstitial atoms) in crystals, and Anderson localization of electrons in disordered media.(1)

2) The usual perception among solid-state researchers is that in perfect lattices -- those free of extrinsic defects -- phonons and electrons exist only in extended, plane wave states. That notion extends to any periodic structure, such as a photonic crystal or a periodic array of optical waveguides. Such firmly entrenched perceptions were severely jolted in the late 1980s by the discovery that intrinsic localized modes(2) (ILMs), also known as "discrete breathers"(3) (DBs), are, in fact, typical excitations in perfectly periodic but strongly nonlinear systems.

3) The past several years have seen this prediction confirmed by a flood of experimental observations of ILMs in physical systems ranging from electronic and magnetic solids, through microengineered structures including Josephson junctions and optical waveguide arrays, to laser-induced photonic crystals. Experimentalists are currently hot on the trail of ILMs in Bose-Einstein condensates (BECs) and biopolymers. Hopes are high that these exotic excitations will be useful in all-optical logic and switching devices and in targeted breaking of chemical bonds, and will prove helpful to the understanding of melting processes in solids and conformational changes in biomolecules.

4) A good working definition of ILMs (or DBs) is that they are spatially localized, time-periodic, and stable (or at least long-lived) excitations in spatially extended, perfectly periodic, discrete systems. The existence of two distinct names for the same phenomenon is an indication that separate historical paths led to their discovery and provides key insights into the reasons for their existence. A DB (discrete breather) is a localized, oscillatory excitation that is stabilized against decay by the discrete nature of the periodic lattice. An ILM (intrinsic localized mode) is an excitation that is localized in space by the intrinsic nonlinearity of the medium, rather than by a defect or impurity.

5) By the early 1990s, researchers following these two paths had converged on the insight that stable localized periodic modes, whether called ILMs or DBs, were generic excitations in discrete nonlinear systems, and that to study them systematically, one should start with a system of uncoupled nonlinear oscillators --the "anti-continuum limit" -- and treat the coupling as a weak perturbation.(2-5)

References (abridged):

1. A. A. Maradudin, E. W. Montroll, G. H. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation, Academic, New York (1963); P. W. Anderson, Phys. Rev. 109, 1492 (1958) [CAS].

2. A. S. Dolgov, Sov. Phys. Solid State 28, 907 (1986); A. J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988); see also http://www.lassp.cornell.edu/~sievers/ilm/bibl

3. S. Flach, C. R. Willis, Phys. Rep. 295, 181 (1998); O. Braun, Yu. S. Kivshar, Phys. Rep. 306, 1 (1998) , chap. 6. See also the articles in the focus issue on "Nonlinear Localized Modes: Physics and Applications," Chaos 13, 586 (2003)

4. R. T. Birge, H. Spooner, Phys. Rev. 28, 259 (1926) ; J. W. Ellis, Phys. Rev. 33, 27 (1929) ; B. R. Henry, W. Siebrand, J. Chem. Phys. 49, 5369 (1968); A. A. Ovchinnikov, Sov. Phys. JETP 30, 147 (1970); R. Bruinsma et al., Phys. Rev. Lett. 57, 1773 (1986); A. S. Davydov, Solitons in Molecular Systems, E. S. Kryachko, trans., Kluwer, Hingham, Mass. (1985)

5. R. S. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994); S. Aubry, Physica D 103, 201 (1997); Y. Zolotaryuk et al., Phys. Rev. B 63, 214422 (2001)

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