Understanding excitons using spherical geometry

Abstract

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 \alert{the} exact results for a wide range of $\epsilon$ values.

5 pages, 4 figures and 2 tables, accepted for publication in Phys. Lett. A

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Cited by in corpus (6)

• Green functions and self-consistency: insights from the spherium model
• Uniform electron gases. I. Electrons on a ring
• Two-electron atom with a screened interaction
• Nodal surfaces and interdimensional degeneracies
• Uniform electron gases: III. Low-density gases on three-dimensional spheres
• Transient Uniform Electron Gases