DIMENSIONALITY DEPENDENCE IN SELF-TRAPPING OF EXCITONS

Self-trapping (ST) of excitons (or electrons) interacting with phonons via short-range potentials depends strongly on the degree of freedom of their motion on the lattice. When excitons can move three-dimensionally, the self-trapped (S) state appears suddenly as a strongly-localized one when the coupling constant (g) exceeds a certain critical value. Free (F) states do not become unstable however large g is. When exciton motion is limited only in one dimension, excitons are always self-trapped and F states are unstable irrespective of the magnitude of g(not-equal 0). The S state appears as a strongly-extended one in the limit of g-->0, and its spatial extension decreases as g increases. For excitons mobile in two dimensions, there exist two critical values g(c1) and g(c2)(>g(c1)) of g: The S state appears suddenly as a strongly-localized one when g exceeds g(c1), but F states become unstable when g exceeds g(c2) although they are metastable for g(c1) < g < g(c2).