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 (≠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 .