On the theory of wannier exciton in a disordered structure

Abstract

The motion of the optically excited coulomb-bounded electron-hole pair in a random gaussian potential has been investigated by using the Feynman path integral method. The motion of the mass center shows the same hopping character as a single particle. The coupling of the mass center motion and of the internal motion of the pair depends on the difference of the effective masses; ifme=mh or ifme≪mh the coupling tends to zero. A characteristic function\(F(\omega ) = \left( {1 - \frac{{\omega _c^2 }}{{2\omega ^2 }}\frac{{\phi \hbar \beta }}{{tg\frac{{\phi \hbar \beta }}{2}}}} \right)^{ - 1} \) has been found which determines the influence of the disorder on the internal motion of the pair. IfF(ω)→ 0 the motion is hydrogen-like, ifF(ω)→∞ the pair dissociates. The conditions for dominancy of the localizing influence of the random field or of the hydrogenlike motion due to the coulombic bound has been found. It has been shown that at high temperatures one can speak about the Wannier exciton at the same sense as in periodic lattices.