1112.5313 (Pierre-François Loos)

Understanding excitons using the spherical geometry    [PDF]

Pierre-François Loos

Using the spherical geometry, we introduce a novel model to study excitons confined in a three-dimensional space, which offers unparalleled mathematical simplicity while retaining much of the key physics. This new model consists of an exciton trapped on the 3-sphere (i.e. the surface of a four-dimensional ball), and provides a unified treatment of Frenkel and Wannier-Mott excitons. Moreover, we show that one can determine, for particular values of the dielectric constant $\epsilon$, the closed-form expression of the exact wave function. We use the exact wave function of the lowest bound state for $\epsilon=2$ to introduce an intermediate regime which gives satisfactory agreement with exact diagonalization results for a wide range of $\epsilon$ values.

View original: http://arxiv.org/abs/1112.5313