Editing Exciton (section)

== Self-trapping of excitons==
In crystals, excitons interact with phonons, the lattice vibrations. If this coupling is weak as in typical semiconductors such as GaAs or Si, excitons are scattered by phonons. However, when the coupling is strong, excitons can be self-trapped.<ref>N. Schwentner, E.-E. Koch, and J. Jortner, Electronic excitations in condensed rare gases,  Springer tracts in modern physics, '''107''', p. 1 (1985).</ref><ref>M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa, and E. Hanamura. Excitonic Processes in Solids, Springer Series in Solid State Sciences, Vol. '''60''' (1986).</ref> '''Self-trapping''' results in dressing excitons with a dense cloud of virtual phonons which strongly suppresses the ability of excitons to move across the crystal. In simpler terms, this means a local deformation of the crystal lattice around the exciton. Self-trapping can be achieved only if the energy of this deformation can compete with the width of the exciton band. Hence, it should be of atomic scale, of about an electron volt.

Self-trapping of excitons is similar to forming strong-coupling [[polaron]]s but with three essential differences. First, self-trapped exciton states are always of a small radius, of the order of lattice constant, due to their electric neutrality. Second, there exists a '''self-trapping barrier''' separating free and self-trapped states, hence, free excitons are metastable. Third, this barrier enables '''coexistence of free and self-trapped states''' of excitons.<ref>E. I. Rashba, "Theory of Strong Interaction of Electron Excitations with Lattice Vibrations in Molecular Crystals", Optika i Spektroskopiya '''2''', pp. 75, 88 (1957).</ref><ref>E. I. Rashba, Self-trapping of excitons, in: Excitons (North-Holland, Amsterdam, 1982), p. 547.</ref><ref>S. I. Pekar, E. I. Rashba, V. I. Sheka, Soviet Physics JETP '''49''', p. 251 (1979), http://www.jetp.ac.ru/cgi-bin/dn/e_049_01_0129.pdf {{Webarchive|url=https://web.archive.org/web/20190223074133/http://www.jetp.ac.ru/cgi-bin/dn/e_049_01_0129.pdf|date=2019-02-23}}.</ref> This means that spectral lines of free excitons and wide bands of self-trapped excitons can be seen simultaneously in absorption and luminescence spectra. While the self-trapped states are of lattice-spacing scale, the barrier has typically much larger scale. Indeed, its spatial scale is about <math>r_b\sim m\gamma^2/\omega^2</math> where <math>m</math> is effective mass of the exciton, <math>\gamma</math> is the exciton-phonon coupling constant, and <math>\omega</math> is the characteristic frequency of optical phonons. Excitons are self-trapped when <math>m</math> and <math>\gamma</math> are large, and then the spatial size of the barrier is large compared with the lattice spacing. Transforming a free exciton state into a self-trapped one proceeds as a collective tunneling of coupled exciton-lattice system (an [[instanton]]). Because <math>r_b</math> is large, tunneling can be described by a continuum theory.<ref>{{Cite book |last1=Kagan |first1=Yu |url=https://books.google.com/books?id=ElDtL9qZuHUC&dq=%22E+I+Rashba%22&pg=PA347 |title=Quantum Tunnelling in Condensed Media |last2=Leggett |first2=A. J. |date=2012-12-02 |publisher=Elsevier |isbn=978-0-444-60047-9 |language=en}}</ref> The height of the barrier <math>W\sim \omega^4/m^3\gamma^4</math>. Because both <math>m</math> and <math>\gamma</math> appear in the denominator of <math>W</math>, the barriers are basically low. Therefore, free excitons can be seen in crystals with strong exciton-phonon coupling only in pure samples and at low temperatures. Coexistence of free and self-trapped excitons was observed in rare-gas solids,<ref>{{Cite book |url=https://searchworks.stanford.edu/view/1269574 |title=Excited-state spectroscopy in solids: Varenna on Lake Como, Villa Monastero, 9–19 July 1985 |date=1987 |publisher=North-Holland |isbn=978-0-444-87070-4 |editor-last=Grassano |editor-first=U. M. |series=Proceedings of the International School of Physics "Enrico Fermi" |location=Amsterdam ; New York |at=Course 96 |language=en |editor-last2=Terzi |editor-first2=N. |editor-last3=Società italiana di fisica}}</ref><ref>I. Ya. Fugol', "Free and self-trapped excitons in cryocrystals: kinetics and relaxation processes." Advances in Physics '''37''', pp. 1–35 (1988).</ref> alkali-halides,<ref>Ch. B. Lushchik, in "Excitons,"  edited by E. I. Rashba, and M. D. Sturge, (North Holland,  Amsterdam, 1982), p. 505.</ref> and in molecular crystal of pyrene.<ref>M. Furukawa, Ken-ichi Mizuno, A. Matsui, N. Tamai and I. Yamazaiu, Branching of Exciton Relaxation to the Free and Self-Trapped Exciton States, Chemical Physics '''138''', p. 423 (1989).</ref>