Exact polarizability of low-dimensional excitons

Wannier excitons polarized by a static electric field and confined to low-dimensional structures are studied. Effective non-integer dimensions are included by considering hydrogenic states in α-dimensional space, with α as a parameter. Exact expressions for lowest order energy and wave function corrections are obtained as a function of α. For the 1s state, we demonstrate that the exciton polarizability decreases with reduced dimensionality and eventually vanishes as (α−1)⁴ as the 1D limit is approached. The low-dimensional 2s and 2p polarizabilities are also decreased but remain finite in the 1D limit.